Newtonian Mechanics

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null Cover Half Title Title Copyright Contents Preface Chapter 1: Mechanical Models 1.1 Introduction 1.2 Models 1.3 Estimates 1.4 Units and Dimensions 1.5 Equations 1.6 Chapter Summary Chapter 2: Forces 2.1 Action and Reaction 2.2 Forces in Equilibrium 2.3 Horse Before Cart 2.4 Static Friction 2.5 Sliding Friction 2.6 A Friction Paradox 2.7 Rolling Friction 2.8 Contact Area 2.9 Torque: The Moment or Couple of a Force 2.10 Condition for Static Equilibrium 2.11 Center of Gravity 2.12 An Example 2.13 Problem Summary 2.14 Inclined Planes 2.15 Pulling at an Angle on a Flat Plane 2.16 Pulling at an Angle on an Inclined Plane 2.17 Solution of Problem 2 2.18 Tipping Point 2.19 Tipping on an Inclined Plane 2.20 Levers 2.21 Stress and Strain 2.22 Chapter Summary 2.23 Exercises Chapter 3: Kinematics 3.1 Constant Speed 3.2 Constant Acceleration 3.3 Example: A Body Projected Vertically Under Gravity 3.4 Motion in Two Dimensions 3.5 Addition of Velocities 3.6 Projectile Motion 3.7 Approximate Solutions 3.8 Air Resistance 3.9 Addition of Accelerations 3.10 Other Forms of Acceleration 3.11 Chapter Summary 3.12 Exercises Chapter 4: Energy 4.1 Work 4.2 Kinetic Energy and Work 4.3 Definition of Mass 4.4 Work and Potential Energy 4.5 Conservative Forces 4.6 Non-Conservative Forces 4.7 Friction and “Zero Work Forces” 4.8 Conservation of Energy 4.9 Units for Energy 4.10 Example 4.11 Bound Systems 4.12 Virtual Work 4.13 Elastic Energy 4.14 Example - Bungee Jumping 4.15 Solution to the Problem 4.16 Chapter Summary 4.17 Exercises Chapter 5: Motion 5.1 Newtonian Dynamics 5.2 Equations of Motion 5.3 An Example 5.4 Motion in Higher Dimensions 5.5 Rate of Doing Work 5.6 Inertial Forces 5.7 Systems of Particles 5.8 Example: Motion Under Air Resistance 5.9 Sky Dive 5.10 Tower Problem 5.11 Model 1 5.12 Model 2: Terminal Speed 5.13 Model 3 5.14 The Shape of the Shot 5.15 Upthrust 5.16 Simple Harmonic Motion 5.17 Why SHM is Important 5.18 Energy of a Harmonic Oscillator 5.19 Chapter Summary 5.20 Exercises Chapter 6: Momentum 6.1 Conservation 6.2 Conservation and Invariance 6.3 Impulse 6.4 Collisions in One Dimension 6.5 Center of Mass Frame 6.6 Inelastic Collisions 6.7 The Problem 6.8 Collisions in 2 Dimensions 6.9 Collision Timescales 6.10 Rocket Equation 6.11 Chapter Summary 6.12 Exercises Chapter 7: Orbital Motion 7.1 Angular Speed: Geometric Approach 7.2 Angular Speed: Algebraic Approach 7.3 Angular Velocity as a Vector 7.4 Angular Acceleration: Geometric Approach 7.5 Angular Acceleration: Algebraic Approach 7.6 Angular Momentum 7.7 Circular Motion: Dynamics 7.8 Particle in a Magnetic Field 7.9 Centrifugal Force 7.10 Rotating Frames 7.11 Gravity 7.12 Extended Bodies 7.13 Gravitational Potential and Potential Energy 7.14 Escape Speed 7.15 Radial Infall 7.16 Circular Orbits 7.17 Virial Theorem 7.18 Changing Orbits 7.19 Elliptical Orbits 7.20 Properties of the Ellipse 7.21 Kepler’s Laws 7.22 Derivation of Kepler’s Laws for Elliptical Orbits 7.23 Extended Bodies: Multipole Expansion 7.24 The Poisson Equation 7.25 Motion Inside Matter: Falling Through the Earth 7.26 Tidal Forces 7.27 Solution of the Problem: Roche Limit 7.28 What is Gravity? 7.29 Chapter Summary 7.30 Exercises Chapter 8: Oscillations 8.1 Resonance 8.2 Damping 8.3 Quality Factor 8.4 Forced Oscillations 8.5 Impedance 8.6 Energy and Phase 8.7 Power Curve 8.8 Complex Exponentials 8.9 Fourier Analysis 8.10 Coupled Oscillators 8.11 Coupled Oscillators with Dissipation 8.12 Forced Coupled Oscillators 8.13 Chapter Summary 8.14 Exercises Chapter 9: Rigid Bodies 9.1 Rotational Energy 9.2 Moments of Inertia 9.3 Angular Momentum 9.4 The Receding Moon 9.5 Space Tether 9.6 Equation of Motion 9.7 Compound Pendulum 9.8 A Model of Running 9.9 Rolling and Slipping 9.10 Galileo’s Inclined Plane 9.11 Spin and Precession 9.12 Euler Equations 9.13 Chapter Summary 9.14 Exercises Chapter 10: Stability of Motion 10.1 Perturbations 10.2 Cubic Potential 10.3 Motion of the Planet Mercury 10.4 Stability: General Formulation 10.5 An Example of Stability: Non-Newtonian Orbits 10.6 A Warning 10.7 Solution to Problem 10.8 Phase Portraits: Harmonic Oscillator 10.9 Phase Portraits: Damped Oscillator 10.10 Chaos 10.11 Chapter Summary 10.12 Exercises Chapter 11: Lagrangian and Hamiltonian Mechanics 11.1 Principle of Least Action 11.2 Euler-Lagrange Equations 11.3 Newton’s Laws 11.4 Simple Harmonic Oscillator 11.5 Acceleration in Polar Coordinates 11.6 Rotating Coordinate System 11.7 Bead on a Wire 11.8 Cycloidal Pendulum 11.9 Spherical Pendulum 11.10 Compound Pendulum 11.11 Small Oscillations Revisited 11.12 An Example 11.13 Hamiltonian Mechanics 11.14 Conservation Laws and Noether’s Theorem 11.15 Action Angle Variables and Integrable Systems 11.16 Quantum Theory 11.17 Chapter Summary 11.18 Exercises Index