Statics and Dynamics Demystified

The fast and easy way to learn statics and dynamics This new title in the popular Demystified series offers practical, easy-to-follow coverage of the difficult statics and dynamics course. Expert author David McMahon follows the standard curriculum, starting with basic mathematical concepts and moving on to advanced topics such as Newton's Law, structural analysis, centrifugal forces, kinematics, and the LaGrange method.

David McMahon is a physicist and researcher at Sandia National Laboratories. He is the author of Linear Algebra Demystified, Quantum Mechanics Demystified, and Relativity Demystified.

Preface

ix

A Review of Vector Calculus

1

(35)

Introduction

1

(1)

Basic Operations on Vectors

2

(1)

The Dot Product

3

(2)

The Vector Cross Product

5

(1)

Vector Triple Products

6

(1)

The Cylindrical and Spherical Coordinate Systems

7

(1)

The Position Vector

8

(1)

The Gradient

9

(5)

The Operator and Divergence

14

(3)

The Curl

17

(1)

The Laplacian

18

(2)

Vector Identities

20

(1)

Line Integrals

21

(4)

Conservative Vector Fields

25

(3)

Surface Integrals

28

(7)

Quiz

35

(1)

Particles and Forces

36

(13)

Characterizing Motion

36

(1)

Newton's First Law

37

(1)

Newton's Second Law

38

(1)

Newton's Third Law

39

(1)

Couple

39

(1)

Deriving Newton's First Law

39

(4)

Line of Action

43

(1)

Forces and Moments

43

(5)

Quiz

48

(1)

Resultants, Equilibrium, and Statics

49

(12)

Resultants

49

(3)

Static Equilibrium

52

(7)

Quiz

59

(2)

Gravity

61

(12)

The Gravitational Force

61

(4)

Gravitational Acceleration

65

(2)

The Law of Periods

67

(1)

The Gravitational Potential

68

(4)

Quiz

72

(1)

Moments of Inertia

73

(20)

Moment

73

(2)

Arbitrary Fulcrum and Center of Mass

75

(3)

Continuous Systems

78

(4)

Second Moments, Moment of Inertia of an Area

82

(2)

Moment of Inertia for Mass

84

(6)

Radius of Gyration

90

(1)

Parallel Axis Theorem

91

(1)

Quiz

91

(2)

Cables

93

(6)

Cables

93

(1)

Endpoint Tension in Cables

94

(1)

Length of a Suspension Cable

95

(1)

Catenary Cables

96

(1)

Quiz

97

(2)

Friction

99

(12)

Belt Friction

107

(2)

Rolling Resistance

109

(1)

Quiz

110

(1)

Particle Kinematics

111

(17)

Rectilinear Particle Motion

111

(2)

Constant Acceleration

113

(5)

Particle Motion in Higher Dimensions

118

(4)

Projectile Motion

122

(3)

Uniform Circular Motion

125

(1)

Quiz

126

(2)

Dynamics and Newton's Second Law

128

(28)

Linear Momentum

128

(2)

Newton's Laws of Motion

130

(1)

The First Law of Motion

131

(1)

The Second Law of Motion

131

(2)

The Third Law of Motion

133

(10)

Dynamics and Kinetic Friction

143

(2)

Force and Potential Energy

145

(2)

The Harmonic Oscillator

147

(4)

Damping

151

(3)

Quiz

154

(2)

Circular Motion

156

(15)

Uniform Circular Motion Revisited

156

(7)

Kinetic Energy of Rotation

163

(1)

Angular Momentum and Torque

164

(5)

Quiz

169

(2)

Energy and Work

171

(17)

Potential and Kinetic Energy

171

(2)

Forces and Work

173

(3)

The Work-Energy Theorem

176

(3)

Energy and Momentum

179

(1)

Power

180

(2)

Efficiency

182

(1)

Basic Conservation Laws

183

(4)

Quiz

187

(1)

Waves and Vibrations

188

(21)

Basic Wave Motion

188

(2)

Sinusoidal Waves

190

(4)

Dispersion

194

(3)

Superposition and Interference

197

(2)

Energy and Power in Waves

199

(3)

Vibrations

202

(6)

Quiz

208

(1)

Advanced Mechanics

209

(14)

The Lagrangian

209

(4)

Systems in Multiple Dimensions

213

(6)

The Hamiltonian

219

(3)

Quiz

222

(1)

Final Exam

223

(7)

Quiz Solutions and Final Exam Answers

230

(7)

Quiz Solutions

230

(4)

Final Exam Answers

234

(3)

Bibliography

237

(2)

Index

239

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Statics and Dynamics Demystified

Summary

Author Biography

Table of Contents

Supplemental Materials