Loading...Statics and Dynamics Demystified
David McMahon
CONTENTS
Preface ix
A Review of Vector Calculus
Introduction
Basic Operations on Vectors
The Dot Product
The Vector Cross Product
Vector Triple Products
The Cylindrical and Spherical Coordinate
Systems
The Position Vector
The Gradient
The V Operator and Divergence
The Curl
The Laplacian
Vector Identities
Line Integrals
Conservative Vector Fields
Surface Integrals
Quiz
CHAPTER 1
Particles and Forces
Characterizing Motion
CHAPTER 2 36
36
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vi Statics and Dynamics Demystified
Newton’s First Law
Newton’s Second Law
Newton’s Third Law
Couple
Deriving Newton’s First Law
Line of Action
Forces and Moments
Quiz
Resultants, Equilibrium, and Statics
Resultants
Static Equilibrium
Quiz
CHAPTER 3
Gravity
The Gravitational Force
Gravitational Acceleration
The Law of Periods
The Gravitational Potential
Quiz
CHAPTER 4
Moments of Inertia
Moment
Arbitrary Fulcrum and Center of Mass
Continuous Systems
Second Moments, Moment of Inertia
of an Area
Moment of inertia for Mass
Radius of Gyration
Parallel Axis Theorem
Quiz
CHAPTER 5
Cables
Cables
Endpoint Tension in Cables
CHAPTER 6
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Length of a Suspension Cable
Catenary Cables
Quiz 97
Friction
Belt Friction
Rolling Resistance
Quiz
CHAPTER 7
Particle Kinematics
Rectilinear Particle Motion
Constant Acceleration
Particle Motion in Higher Dimensions
Projectile Motion
Uniform Circular Motion
Quiz
CHAPTER 8
Dynamics and Newton’s Second Law
Linear Momentum
Newton’s Laws of Motion
The First Law of Motion
The Second Law of Motion
The Third Law of Motion
Dynamics and Kinetic Friction
Force and Potential Energy
The Harmonic Oscillator
Damping
Quiz
CHAPTER 9
Circular Motion
Uniform Circular Motion Revisited
Kinetic Energy of Rotation
Angular Momentum and Torque
Quiz
CHAPTER 10
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viii Statics and Dynamics Demystified
Energy and Work
Potential and Kinetic Energy
Forces and Work
The Work-Energy Theorem
Energy and Momentum
Power
Efficiency
Basic Conservation Laws
Quiz
CHAPTER 11
Waves and Vibrations
Basic Wave Motion
Sinusoidal Waves
Dispersion
Superposition and Interference
Energy and Power in Waves
Vibrations
Quiz
CHAPTER 12
Advanced Mechanics
The Lagrangian
Systems in Multiple Dimensions
The Hamiltonian
Quiz
CHAPTER 13
Final Exam 223
Quiz Solutions and Final Exam Answers 230
Quiz Solutions
Final Exam Answers
Bibliography 237
Index 239
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