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An Introduction to Mechanics

Book Description

In the years since it was first published, this classic introductory textbook has established itself as one of the best-known and most highly regarded descriptions of Newtonian mechanics. Intended for undergraduate students with foundation skills in mathematics and a deep interest in physics, it systematically lays out the principles of mechanics: vectors, Newton's laws, momentum, energy, rotational motion, angular momentum and noninertial systems, and includes chapters on central force motion, the harmonic oscillator, and relativity. Numerous worked examples demonstrate how the principles can be applied to a wide range of physical situations, and more than 600 figures illustrate methods for approaching physical problems. The book also contains over 200 challenging problems to help the student develop a strong understanding of the subject. Password-protected solutions are available for instructors at www.cambridge.org/9780521198219.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Dedication
  6. Contents
  7. List of Examples
  8. Preface
  9. To the Teacher
  10. 1. Vectors and Kinematics—A Few Mathematical Preliminaries
    1. 1.1 Introduction
    2. 1.2 Vectors
    3. Definition of a Vector, The Algebra of Vectors
    4. 1.3 Components of a Vector
    5. 1.4 Base Vectors
    6. 1.5 Displacement and the Position Vector
    7. 1.6 Velocity and Acceleration
    8. Motion in One Dimension
    9. Motion in Several Dimensions
    10. A Word about Dimensions and Units
    11. 1.7 Formal Solution of Kinematical Equations
    12. 1.8 More about the Derivative of a Vector
    13. 1.9 Motion in Plane Polar Coordinates
    14. Polar Coordinates
    15. Velocity in Polar Coordinates
    16. Evaluating [(dr/dt)]
    17. Acceleration in Polar Coordinates
    18. Note 1.1 Mathematical Approximation Methods
    19. The Binomial Series
    20. Taylor’s Series
    21. Differentials
    22. Some References To Calculus Texts
    23. Problems
  11. 2. Newton’s Laws—The Foundations of Newtonian Mechanics
    1. 2.1 Introduction
    2. 2.2 Newton’s Laws
    3. Newton’s First Law
    4. Newton’s Second Law
    5. Newton’s Third Law
    6. 2.3 Standards and Units
    7. The Fundamental Standards
    8. Systems of Units
    9. 2.4 Some Applications of Newton’s Laws
    10. 2.5 The Everyday Forces of Physics
    11. Gravity, Weight, and the Gravitational Field
    12. The Electrostatic Force
    13. Contact Forces
    14. Tension—The Force of a String
    15. Tension and Atomic Forces
    16. The Normal Force
    17. Friction
    18. Viscosity
    19. The Linear Restoring Force: Hooke’s Law, the Spring, and Simple Harmonic Motion
    20. Note 2.1 the Gravitational Attraction of a Spherical Shell
    21. Problems
  12. 3. Momentum
    1. 3.1 Introduction
    2. 3.2 Dynamics of a System of Particles
    3. Center of Mass
    4. 3.3 Conservation of Momentum
    5. Center of Mass Coordinates
    6. 3.4 Impulse and a Restatement of the Momentum Relation
    7. 3.5 Momentum and the flow of Mass
    8. 3.6 Momentum Transport
    9. Note 3.1 Center of Mass
    10. Problems
  13. 4. Work and Energy
    1. 4.1 Introduction
    2. 4.2 Integrating the equation of Motion in One Dimension
    3. 4.3 The Work-Energy Theorem in One Dimension
    4. 4.4 Integrating the equation of Motion in Several Dimensions
    5. 4.5 The Work-Energy Theorem
    6. 4.6 Applying the Work-Energy Theorem
    7. 4.7 Potential Energy
    8. Illustrations of Potential Energy
    9. 4.8 What Potential Energy tells us about Force
    10. Stability
    11. 4.9 Energy Diagrams
    12. 4.10 Small Oscillations in a Bound System
    13. 4.11 Nonconservative Forces
    14. 4.12 The General Law of Conservation of Energy
    15. 4.13 Power
    16. 4.14 Conservation Laws and Particle Collisions
    17. Collisions and Conservation Laws
    18. Elastic and Inelastic Collisions
    19. Collisions in One Dimension
    20. Collisions and center of Mass Coordinates
    21. Problems
  14. 5. Some Mathematical aspects of force and Energy
    1. 5.1 Introduction
    2. 5.2 Partial Derivatives
    3. 5.3 How to find the force if you know the Potential Energy
    4. 5.4 The Gradient Operator
    5. 5.5 The Physical meaning of the Gradient
    6. Constant Energy Surfaces and Contour Lines
    7. 5.6 How to find out if a Force is Conservative
    8. 5.7 Stokes’ Theorem
    9. Problems
  15. 6. Angular Momentum and Fixed axis Rotation
    1. 6.1 Introduction
    2. 6.2 Angular Momentum of a Particle
    3. 6.3 Torque
    4. 6.4 Angular Momentum and Fixed axis Rotation
    5. 6.5 Dynamics of Pure Rotation about an axis
    6. 6.6 The Physical Pendulum
    7. The Simple Pendulum
    8. The Physical Pendulum
    9. 6.7 Motion Involving both Translation and Rotation
    10. The Work-Energy Theorem
    11. 6.8 The Bohr Atom
    12. Note 6.1 Chasles’ Theorem
    13. Note 6.2 Pendulum Motion
    14. Problems
  16. 7. Rigid Body Motion and the Conservation of Angular Momentum
    1. 7.1 Introduction
    2. 7.2 The Vector Nature of angular Velocity and Angular Momentum
    3. 7.3 The Gyroscope
    4. 7.4 Some Applications of Gyroscope Motion
    5. 7.5 Conservation of Angular Momentum
    6. 7.6 Angular Momentum of a Rotating Rigid Body
    7. Angular Momentum and the Tensor of Inertia
    8. Principal Axes
    9. Rotational Kinetic Energy
    10. Rotation about a Fixed Point
    11. 7.7 Advanced Topics in the Dynamics of Rigid body Rotation
    12. Introduction
    13. Torque-Free Precession: Why the Earth Wobbles
    14. Euler’s Equations
    15. Note 7.1 Finite and Infinitesimal Rotations
    16. Note 7.2 More about Gyroscopes
    17. Case 1 Uniform Precession
    18. Case 2 Torque-Free Precession
    19. Case 3 Nutation
    20. Problems
  17. 8. Noninertial Systems and Fictitious Forces
    1. 8.1 Introduction
    2. 8.2 The Galilean Transformations
    3. 8.3 Uniformly Accelerating Systems
    4. 8.4 The Principle of Equivalence
    5. 8.5 Physics in a Rotating coordinate System
    6. Time Derivatives and Rotating Coordinates
    7. Acceleration Relative to Rotating Coordinates
    8. The Apparent Force in a Rotating coordinate System
    9. Note 8.1 the Equivalence Principle and the Gravitational Red Shift
    10. Note 8.2 Rotating Coordinate Transformation
    11. Problems
  18. 9. Central Force Motion
    1. 9.1 Introduction
    2. 9.2 Central Force Motion as a One body Problem
    3. 9.3 General Properties of central Force Motion
    4. The Motion Is Confined to a Plane
    5. The Energy and Angular Momentum Are Constants of the Motion
    6. The Law of Equal Areas
    7. 9.4 Finding the Motion in Real Problems
    8. 9.5 The Energy equation and Energy Diagrams
    9. 9.6 Planetary Motion
    10. 9.7 Kepler’s Laws
    11. Note 9.1 Properties of the Ellipse
    12. Problems
  19. 10. The Harmonic Oscillator
    1. 10.1 Introduction and Review
    2. Standard form of the Solution
    3. Nomenclature
    4. Energy Considerations
    5. Time Average Values
    6. Average Energy
    7. 10.2 The Damped Harmonic Oscillator
    8. Energy
    9. The Q of an Oscillator
    10. 10.3 The Forced Harmonic Oscillator
    11. The Undamped Forced Oscillator
    12. Resonance
    13. The Forced Damped Harmonic Oscillator
    14. Resonance in a Lightly Damped System: The Quality Factor Q
    15. 10.4 Response in time Versus Response in Frequency
    16. Note 10.1 Solution of the equation of Motion for the Undriven Damped Oscillator
    17. The use of Complex Variables
    18. The Damped Oscillator
    19. Note 10.2 Solution of the equation of Motion for the Forced Oscillator
    20. Problems
  20. 11. The Special Theory of Relativity
    1. 11.1 The need for a new Mode of thought
    2. 11.2 The Michelson-Morley Experiment
    3. 11.3 The Postulates of Special Relativity
    4. The Universal Velocity
    5. The Principle of Relativity
    6. The Postulates of Special Relativity
    7. 11.4 The Galilean Transformations
    8. 11.5 The Lorentz Transformations
    9. Problems
  21. 12. Relativistic Kinematics
    1. 12.1 Introduction
    2. 12.2 Simultaneity and the order of Events
    3. 12.3 The Lorentz Contraction and time Dilation
    4. The Lorentz Contraction
    5. Time Dilation
    6. 12.4 The Relativistic Transformation of Velocity
    7. 12.5 The Doppler Effect
    8. The Doppler shift in Sound
    9. Relativistic Doppler Effect
    10. The Doppler effect for an observer off the line of Motion
    11. 12.6 The Twin Paradox
    12. Problems
  22. 13. Relativistic Momentum and Energy
    1. 13.1 Momentum
    2. 13.2 Energy
    3. 13.3 Massless Particles
    4. 13.4 Does Light Travel at the Velocity of Light?
    5. Problems
  23. 14. Four-Vectors and Relativistic Invariance
    1. 14.1 Introduction
    2. 14.2 Vectors and Transformations
    3. Rotation about the Z Axis
    4. Invariants of a Transformation
    5. The Transformation Properties of Physical Laws
    6. Scalar Invariants
    7. 14.3 Minikowski Space and Four-Vectors
    8. 14.4 the Momentum-Energy Four-Vector
    9. 14.5 Concluding Remarks
    10. Problems
  24. Index