The Physics of Sports
, by Lisa, Michael
- ISBN: 9780073513973 | 0073513970
- Cover: Paperback
- Copyright: 2/20/2015
Preface to the studentPreface to the instructor I Primary Chapters 1 Warm-up: Basic concepts 1.1 Quantifying the world of sports Units, conversions, scientific notation 1.2 When we don’t have exact numbers Estimation, typical scales 1.3 The center of mass Center of massProblems 2 Racing, mathematically1D kinematics 2.1 Phelps in BeijingSpeed, velocity, position and graphs 2.2 Bolt in BerlinAcceleration, constant acceleration kinematics 2.3 Rope-climbing and divingVertical motion and gravity Problems 3 Net Force: Dwight Howard illustratesForces, dynamics 3.1 The Physics of a Dwight Howard Dunk 3.1.1 Waiting for the passWeight, ground reaction force, equilibrium, free-body diagrams, Newton’s first law 3.1.2 Spec sheetWeight and mass 3.1.3 The launchNewton’s 2nd and 3rd Laws; dynamics of a jump; dynamics with non-constant forces; ground reaction force 3.1.4 The flightFreefall dynamics, revisited 3.1.5 The landingCushioning limitations, GRF revisited 3.2 Sideways tractionFriction 3.3 More complex situations2D dynamics and applications 3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
I Primary Chapters 1 Warm-up: Basic concepts 1.1 Quantifying the world of sports Units, conversions, scientific notation 1.2 When we don’t have exact numbers Estimation, typical scales 1.3 The center of mass Center of massProblems 2 Racing, mathematically1D kinematics 2.1 Phelps in BeijingSpeed, velocity, position and graphs 2.2 Bolt in BerlinAcceleration, constant acceleration kinematics 2.3 Rope-climbing and divingVertical motion and gravity Problems 3 Net Force: Dwight Howard illustratesForces, dynamics 3.1 The Physics of a Dwight Howard Dunk 3.1.1 Waiting for the passWeight, ground reaction force, equilibrium, free-body diagrams, Newton’s first law 3.1.2 Spec sheetWeight and mass 3.1.3 The launchNewton’s 2nd and 3rd Laws; dynamics of a jump; dynamics with non-constant forces; ground reaction force 3.1.4 The flightFreefall dynamics, revisited 3.1.5 The landingCushioning limitations, GRF revisited 3.2 Sideways tractionFriction 3.3 More complex situations2D dynamics and applications 3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
1.1 Quantifying the world of sports Units, conversions, scientific notation 1.2 When we don’t have exact numbers Estimation, typical scales 1.3 The center of mass Center of massProblems 2 Racing, mathematically1D kinematics 2.1 Phelps in BeijingSpeed, velocity, position and graphs 2.2 Bolt in BerlinAcceleration, constant acceleration kinematics 2.3 Rope-climbing and divingVertical motion and gravity Problems 3 Net Force: Dwight Howard illustratesForces, dynamics 3.1 The Physics of a Dwight Howard Dunk 3.1.1 Waiting for the passWeight, ground reaction force, equilibrium, free-body diagrams, Newton’s first law 3.1.2 Spec sheetWeight and mass 3.1.3 The launchNewton’s 2nd and 3rd Laws; dynamics of a jump; dynamics with non-constant forces; ground reaction force 3.1.4 The flightFreefall dynamics, revisited 3.1.5 The landingCushioning limitations, GRF revisited 3.2 Sideways tractionFriction 3.3 More complex situations2D dynamics and applications 3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
1.3 The center of mass Center of massProblems 2 Racing, mathematically1D kinematics 2.1 Phelps in BeijingSpeed, velocity, position and graphs 2.2 Bolt in BerlinAcceleration, constant acceleration kinematics 2.3 Rope-climbing and divingVertical motion and gravity Problems 3 Net Force: Dwight Howard illustratesForces, dynamics 3.1 The Physics of a Dwight Howard Dunk 3.1.1 Waiting for the passWeight, ground reaction force, equilibrium, free-body diagrams, Newton’s first law 3.1.2 Spec sheetWeight and mass 3.1.3 The launchNewton’s 2nd and 3rd Laws; dynamics of a jump; dynamics with non-constant forces; ground reaction force 3.1.4 The flightFreefall dynamics, revisited 3.1.5 The landingCushioning limitations, GRF revisited 3.2 Sideways tractionFriction 3.3 More complex situations2D dynamics and applications 3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
2 Racing, mathematically1D kinematics 2.1 Phelps in BeijingSpeed, velocity, position and graphs 2.2 Bolt in BerlinAcceleration, constant acceleration kinematics 2.3 Rope-climbing and divingVertical motion and gravity Problems 3 Net Force: Dwight Howard illustratesForces, dynamics 3.1 The Physics of a Dwight Howard Dunk 3.1.1 Waiting for the passWeight, ground reaction force, equilibrium, free-body diagrams, Newton’s first law 3.1.2 Spec sheetWeight and mass 3.1.3 The launchNewton’s 2nd and 3rd Laws; dynamics of a jump; dynamics with non-constant forces; ground reaction force 3.1.4 The flightFreefall dynamics, revisited 3.1.5 The landingCushioning limitations, GRF revisited 3.2 Sideways tractionFriction 3.3 More complex situations2D dynamics and applications 3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
2.2 Bolt in BerlinAcceleration, constant acceleration kinematics 2.3 Rope-climbing and divingVertical motion and gravity Problems 3 Net Force: Dwight Howard illustratesForces, dynamics 3.1 The Physics of a Dwight Howard Dunk 3.1.1 Waiting for the passWeight, ground reaction force, equilibrium, free-body diagrams, Newton’s first law 3.1.2 Spec sheetWeight and mass 3.1.3 The launchNewton’s 2nd and 3rd Laws; dynamics of a jump; dynamics with non-constant forces; ground reaction force 3.1.4 The flightFreefall dynamics, revisited 3.1.5 The landingCushioning limitations, GRF revisited 3.2 Sideways tractionFriction 3.3 More complex situations2D dynamics and applications 3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
Problems 3 Net Force: Dwight Howard illustratesForces, dynamics 3.1 The Physics of a Dwight Howard Dunk 3.1.1 Waiting for the passWeight, ground reaction force, equilibrium, free-body diagrams, Newton’s first law 3.1.2 Spec sheetWeight and mass 3.1.3 The launchNewton’s 2nd and 3rd Laws; dynamics of a jump; dynamics with non-constant forces; ground reaction force 3.1.4 The flightFreefall dynamics, revisited 3.1.5 The landingCushioning limitations, GRF revisited 3.2 Sideways tractionFriction 3.3 More complex situations2D dynamics and applications 3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
3.1 The Physics of a Dwight Howard Dunk 3.1.1 Waiting for the passWeight, ground reaction force, equilibrium, free-body diagrams, Newton’s first law 3.1.2 Spec sheetWeight and mass 3.1.3 The launchNewton’s 2nd and 3rd Laws; dynamics of a jump; dynamics with non-constant forces; ground reaction force 3.1.4 The flightFreefall dynamics, revisited 3.1.5 The landingCushioning limitations, GRF revisited 3.2 Sideways tractionFriction 3.3 More complex situations2D dynamics and applications 3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
3.1.2 Spec sheetWeight and mass 3.1.3 The launchNewton’s 2nd and 3rd Laws; dynamics of a jump; dynamics with non-constant forces; ground reaction force 3.1.4 The flightFreefall dynamics, revisited 3.1.5 The landingCushioning limitations, GRF revisited 3.2 Sideways tractionFriction 3.3 More complex situations2D dynamics and applications 3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
3.1.4 The flightFreefall dynamics, revisited 3.1.5 The landingCushioning limitations, GRF revisited 3.2 Sideways tractionFriction 3.3 More complex situations2D dynamics and applications 3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
3.2 Sideways tractionFriction 3.3 More complex situations2D dynamics and applications 3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
3.3.1 Dwight Howard takes a quick stepVectors 3.3.2 Football tryoutsTwo moving bodies; how to increase friction 3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
3.3.3 Ball throw speedImportant application 3.4 “Imaginary forces” in sports 3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame 3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force 3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
3.4.3 Discus throwCentripetal and “centrifugal” forces Equations Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
Problems 4 Punts, Dick Fosbury & other projectilesProjectile Motion4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
4.1 The math: simpler than you think2D kinematics 4.2 Football punt: range, hangtime and compromiseRange, hangtime 4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
4.3 Shot putThe range when the starting and ending height are not the same4.4 Human projectilesParabolic motion of CM with changing body shape 4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
4.4.1 The Blake Griffin ballet4.4.2 Dick Fosbury’s Flop 4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
4.4.3 Bob Beamon’s long jump Equations Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
Problems 5 Curveballs, foul shots and bent kicksAerodynamic forces5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.1 Overview4 forces; use of approximations 5.2 Immersion in fluid: BuoyancyBuoyant force 5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity 5.4 Sideward forces from asymmetries 5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness 5.4.2 Bending a ball’s flightMagnus force 5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.5 Aerodynamic forces, one at a timeExamples 5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.5.2 Do we need a computer?Constant-force approximation 5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports 5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot 5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations5.6.1 KnucklingEffects of fluctuating orientation and drag 5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.6.2 Tilting into the wind: discusNon-Magnus lift 5.6.3 Human wings: ski jumpsLift with adjustable tilt 5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules 5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes 5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.7 Not all air is created equalVariations in air density and the effect on sports5.7.1 Rocky Mountain (Natural) HighAltitude and air density 5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.7.2 Hot days are (not) a dragTemperature and air density 5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects 5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
5.7.4 Storm fronts Equations Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
Problems 6 Game changers: collisions in sportsCollisions and momentum6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
6.1 What is a “collision” and how to think about itMomentum, impulse 6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
6.2.1 The energy of a crunchKinetic energy, energy lost 6.2.2 Helmet designImpulse, relation to force 6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
6.2.3 Forcing a runner out of bounds2D inelastic collisions 6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems 6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
6.3.1 Beginner’s first roll - head-on collision1D elastic collisions 6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation 6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
6.3.3 Off-center hits - converting a lily2D elastic collision 6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2 6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system 6.4 A happy medium: dribbling and drivingPartially inelastic collisions 6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution 6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed 6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin 6.5.1 Bounce passtorque from friction; translation & rotation motion 6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
6.5.2 Diving shotAerodynamic and collisional aspects of topspin 6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
Equations Problems 7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity 7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy 7.1.2 Energy during the bounceElastic potential energy 7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
7.1.3 Details of energy during the riseGravitational potential energy 7.2 Efficiencyvarious definitions 7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
7.2.1 The efficiency of a basketball bounce 7.2.2 The efficiency of a golf drive 7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
7.2.3 Heat Death 7.3 The athlete: the energetic starting pointChemical energy and its conversion 7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
7.3.1 The source of energy and its flowFood energy, Calories 7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage 7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes 7.4.1 The water analogy 7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept 7.5 Uncle Rico’s hopes dashedWork, power and the human engine 7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
7.5.1 WorkWork-energy theorem; connection to forces7.5.2 Power 7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
7.5.3 The human engine II - powerCaloric conversion rates 7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion 7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
7.6.1 Work during a lift 7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of movesEquations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
Equations Problems 8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage 8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
8.1.1 The bow’s energyHooke’s Law 8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details 8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
8.2 The Physics of Archery II - Fire PowerOscillation frequency and period 8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details 8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod 8.3.2 How the archer’s paradox worksBuckling, matching timing, details 8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions 8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation 8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
8.5.1 Dangling above the waterTension as an equilibrating force 8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
Equations Problems 9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque 9.1 Input to the bike - sustained human power 9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings 9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency 9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
9.1.3 Power-to-weight ratioPWR 9.2 Power outputPower, force and velocity 9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
9.2.1 HillsGravitational force along a slope 9.2.2 Rolling resistance Dissipation during rolling 9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
9.2.3 Wind dragDrag in still and moving air 9.2.4 The Bicycle Power EquationIterative solution to complicated equations 9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
9.2.5 Cycling versus other modes of transportComparison of power requirements 9.2.6 DraftingAerodynamics of more than one object 9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
9.3 Talansky drives the bikeTorque and rotational motion 9.3.1 RollingConnection between linear and rotational motion 9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence 9.3.3 That annoying 2π – angular velocityAngular velocity, the radian 9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm 9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law 9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle 9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge 9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy Equations Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
Problems 10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
10.1 Human rotationAnatomical axes and moments of inertia 10.2 Backward Giant CircleTorque, energy, rotation around fixed axis 10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
10.2.1 Torques and spin rateTorque changes with lever arm10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
10.2.3 Swinging to speed up10.2.4 Dismount Angular momentum and conservation 10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force 10.4 Rotational Action and Reaction Angular momentum of different body parts 10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis 10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis 10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis Equations Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
Problems II Supplemental Chapters 11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
11 Lines of action on the line of scrimmage: the torque wars 12 A Barry Bonds home run Ball-bat collisions 12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
12.1 Ball-Bat Collision: Speeds, impulse, force 12.2 BBS –Batted Ball Speed 12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
12.3 Focus on the bat Collision with an extended object 12.3.1 Bonds’ swing 12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass 13 The Pole Vault 13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
13.1 Origins 13.2 The modern event 13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
13.2.1 Performance progression 13.2.2 Contributions to height 13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
13.3 Pole Vault 101 –Energy flow 13.3.1 Energy-based estimate of vaulting height 13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
13.3.2 What matters, in the simple calculation 13.4 Pole Vault 102 –Beyond energy flow 13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
13.4.1 Maximizing initial energy - carry weight 13.4.2 Minimizing inelastic energy “loss” 13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
13.4.3 Fully exploiting the energy: flexibility and timing 13.4.4 Work done by the athlete 14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
14 Is it better to run through first base, or to dive? 14.1 The story according to Sport Science 14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
14.2 Too close to call 14.3 Diving speed 14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
14.3.1 “50% deceleration” 14.3.2 Newton’s First Law and air drag 14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
14.4 What’s really happening: Torque and impulse 14.5 Other issues 14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
14.6 Concluding remarks Answers to odd-numbered problemsUnit conversions Tables of relevant physical properties Bibliography, Further Reading Index
Unit conversions Tables of relevant physical properties Bibliography, Further Reading Index
Bibliography, Further Reading Index
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