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The Mechanical Universe

Book Description

This innovative physics textbook intended for science and engineering majors develops classical mechanics from a historical perspective. The presentation of the standard course material includes a discussion of the thought processes of the discoverers and a description of the methods by which they arrived at their theories. However the presentation proceeds logically rather than strictly chronologically, so new concepts are introduced at the natural moment. The book assumes a familiarity with calculus, includes a discussion of rigid body motion, and contains numerous thought-provoking problems. It is largely based in content on The Mechanical Universe: Introduction to Mechanics and Heat, a book designed in conjunction with a tele-course to be offered by PBS in the Fall of 1985. The advanced edition, however, does not coincide exactly with the video lessons, contains additional material, and develops the fundamental ideas introduced in the lower-level edition to a greater degree.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Contents
  5. Preface
  6. Chapter 1 - Introduction to the Mechanical Universe (Program 1)
    1. 1.1 The Copemican Revolution
    2. 1.2 Units and Dimensions
    3. 1.3 A Final Word
  7. Chapter 2 - The Law of Falling Bodies (Program 2)
    1. 2.1 Historical Background
    2. 2.2 Galileo‘s Law
    3. 2.3 Do Heavy Bodies Fall Faster than Light Ones?
    4. 2.4 Medieval Laws of Failing Bodies
    5. 2.5 Experimental Determination of the Law of Falling Bodies
    6. 2.6 The Average Velocity of a Falling Body
    7. 2.7 Instantaneous Velocity: The Derivative
    8. 2.8 Acceleration
    9. 2.9 A Final Word
      1. Problems
  8. Chapter 3 - The Language of Nature: Derivatives and Integrals
    1. 3.1 The Development of Differential Calculus
    2. 3.2 Derivatives and Slopes of Tangent Lines
    3. 3.3 Leibniz’s Notation. Analytic Definition of the Derivative
    4. 3.4 Rules of Differentiation and Derivatives of Special Functions
    5. 3.5 Antidifferentiation, the Reverse of Differentiation
    6. 3.6 Antidifferentiation and Quadrature
    7. 3.7 The Leibniz Integral Notation
    8. 3.8 Applications of the Second Fundamental Theorem to Physics
    9. 3.9 A Final Word
      1. Problems
  9. Chapter 4 - Inertia
    1. 4.1 If the Earth Moves: Aristotelian Objections
    2. 4.2 The Earth Moves: Galileo’s Law of Inertia
    3. 4.3 Relative Motion
    4. 4.4 Projectile Motion: A Consequence of Inertia
    5. 4.5 Calculating a Particular Trajectory
    6. 4.6 A Final Word
      1. Problems
  10. Chapter 5 - Vectors
    1. 5.1 Coordinate Systems
    2. 5.2 Vectors
    3. 5.3 Addition and Subtraction of Vectors, and Multiplication by a Scalar
    4. 5.4 The Scalar Product of Vectors
    5. 5.5 The Cross Product of Vectors
    6. 5.6 Derivatives of Vector Functions in a Fixed Coordinate System
    7. 5.7 Position Vector Expressed in Polar Coordinates
    8. 5.8 Uniform Circular Motion
    9. 5.9 A Final Word
      1. Problems
  11. Chapter 6 - Newton’s Laws and Equilibrium
    1. 6.1 The End of the Confusion
    2. 6.2 Newton’s Laws of Motion
    3. 6.3 Units of Mass, Momentum, and Force
    4. 6.4 Projectile Motion as an Application of Newton’s Second Law
    5. 6.5 Equilibrium: Balance of Forces
    6. 6.6 Equilibrium: Balance of Torques
    7. 6.7 A Final Word
      1. Problems
  12. Chapter 7 - Universal Gravitation and Circular Motion
    1. 7.1 The Genesis of an Idea
    2. 7.2 The Law of Universal Gravitation
    3. 7.3 Acceleration of Gravity on the Earth
    4. 7.4 Why the Moon Doesn’t Fall to the Earth
    5. 7.5 Circular Orbits
    6. 7.6 Other Examples of Uniform Circular Motion
    7. 7.7 A Final Word
      1. Problems
  13. Chapter 8 - Forces
    1. 8.1 The Fundamental Forces: Classification and Unification
    2. 8.2 The Strength of Gravitational and Electric Forces
    3. 8.3 Contact Forces
    4. 8.4 Application of Newton’s Laws
    5. 8.5 Friction
    6. 8.6 Driving on Curved Roadways
    7. 8.7 Motion in a Resistive Medium
    8. 8.8 The Oil-Drop Experiment
    9. 8.9 A Final Word
      1. Problems
  14. Chapter 9 - Forces in Accelerating Reference Frames
    1. 9.1 Inertial and Noninertial Reference Frames
    2. 9.2 Galilean Relativity
    3. 9.3 Inertial Forces
    4. 9.4 Inertial Forces in a Linearly Accelerating Frame
    5. 9.5 Centrifugal Force
    6. 9.6 Effect of the Earth’s Rotation on g
    7. 9.7 Centrifuges
    8. 9.8 A Final Word
      1. Problems
  15. Chapter 10 - Energy: Conservation and Conversion
    1. 10.1 Toward an Idea of Energy
    2. 10.2 Work and Potential Energy
    3. 10.3 Kinetic Energy and the Conservation of Energy
    4. 10.4 Gravitational Potential Energy
    5. 10.5 Potential Energy and Stability
    6. 10.6 Heat and Energy
    7. 10.7 Mechanical Advantage and Efficiency of Machines
    8. 10.8 Power
    9. 10.9 A Final Word
      1. Problems
  16. Chapter 11 - The Conservation of Momentum
    1. 11.1 The Universe as a Machine
    2. 11.2 Newton’s Laws in Retrospect
    3. 11.3 The Center of Mass
    4. 11.4 The Law of Conservation of Momentum
    5. 11.5 Rocket Propulsion
    6. 11.6 Energy and Momentum Conservation in Collisions
    7. 11.7 Center-of-Mass Coordinates
    8. 11.8 Impulse: Collision Forces and Times
    9. 11.9 A Final Word
      1. Problems
  17. Chapter 12 - Oscillatory Motion
    1. 12.1 Finding a Clock That Wouldn’t Get Seasick
    2. 12.2 Simple Harmonic Motion
    3. 12.3 The General Solution of the Differential Equation of Simple Harmonic Motion
    4. 12.4 Examples of Simple Harmonic Oscillators
    5. 12.5 Energy Conservation and Simple Harmonic Motion
    6. 12.6 The Simple Pendulum
    7. 12.7 Gaining Insight Through Approximations
    8. 12.8 Damped Oscillations
    9. 12.9 Forced Oscillations
    10. 12.10 Describing Resonance
    11. 12.11 Damped Forced Oscillations
    12. 12.12 Swinging and Singing Wires in the Wind
    13. 12.13 A Final Word
      1. Problems
  18. Chapter 13 - Angular Momentum
    1. 13.1 Rotary Motion
    2. 13.2 Torque and Angular Momentum
    3. 13.3 Angular Momentum Conservation
    4. 13.4 Force and Torque
    5. 13.5 Kepler’s Law of Equal Areas
    6. 13.6 Vortices and Firestorms
    7. 13.7 Conservation of Angular Momentum and Energy
    8. 13.8 A Final Word
      1. Problems
  19. Chapter 14 - Rotational Dynamics for Rigid Bodies
    1. 14.1 Rotation of a Rigid Body About a Fixed Axis
    2. 14.2 Center of Mass of a Continuous Mass Distribution
    3. 14.3 Moment of Inertia
    4. 14.4 Calculation of Moments of Inertia
    5. 14.5 The Parallel-Axis Theorem
    6. 14.6 Energy and Work in Rigid-Body Rotation
    7. 14.7 Analogies Between Rotational and Translational Motion
    8. 14.8 The Physical Pendulum
    9. 14.9 The Torsion Pendulum
    10. 14.10 Combined Translations and Rotations
    11. 14.11 Kinematics of the Rolling Wheel
    12. 14.12 Rolling Down an Inclined Plane
    13. 14.13 Coriolis Forces
    14. 14.14 A Final Word
      1. Problems
  20. Chapter 15 - Gyroscopes
    1. 15.1 An Ancient Question
    2. 15.2 The Gyroscope
    3. 15.3 Angular Velocity of Precession
    4. 15.4 The Earth as a Gyroscope
    5. 15.5 A Final Word
      1. Problems
  21. Chapter 16 - Kepler’s Laws and the Conic Sections
    1. 16.1 The Quest for Precision
    2. 16.2 Kepler’s Laws
    3. 16.3 Conic Sections
    4. 16.4 The Ellipse
    5. 16.5 The Conics and Eccentricity
    6. 16.6 Properties of the Ellipse
    7. 16.7 Cartesian Equations for Conic Sections
    8. 16.8 A Final Word
      1. Problems
  22. Chapter 17 - Solving the Kepler Problem
    1. 17.1 Setting the Stage
    2. 17.2 Polar Coordinates and the Unit Vectors r and o
    3. 17.3 Solution of the Kepler Problem
    4. 17.4 Celestial Omens: Comets
    5. 17.5 Energy and Eccentricity
    6. 17.6 Orbits and Eccentricity
    7. 17.7 Kepler’s Third Law
    8. 17.8 Planetary Motion and Effective Potential
    9. 17.9 Applications of Orbital Dynamics
    10. 17.10 Calculating the Orbit From Initial Conditions
    11. 17.11 A Final Word
      1. Problems
  23. Chapter 18 - Navigating in Space
    1. 18.1 Freeways in the Sky
    2. 18.2 Navigating in Space
    3. 18.3 Transfer Orbits
    4. 18.4 Gravity Assist
    5. 18.5 A Final Word
      1. Problems
  24. Chapter 19 - Temperature and the Gas Laws
    1. 19.1 Temperature and Pressure
    2. 19.2 The Gas Laws of Boyle, Charles, and Gay-Lussac
    3. 19.3 The Ideal-Gas Law
    4. 19.4 Temperature and Energy
    5. 19.5 A Final Word
      1. Problems
  25. Chapter 20 - The Engine of Nature
    1. 20.1 The Age of Steam
    2. 20.2 Work and the Pressure–Volume Diagram
    3. 20.3 The First Law of Thermodynamics
    4. 20.4 Adiabatic and Isothermal Processes
    5. 20.5 The Second Law of Thermodynamics
    6. 20.6 The Carnot Engine
    7. 20.7 A Final Word
      1. Problems
  26. Chapter 21 - Entropy
    1. 21.1 Toward an Understanding of Entropy
    2. 21.2 Engines and Entropy
    3. 21.3 Entropy and the Second Law of Thermodynamics
    4. 21.4 An Implication of the Entropy Principle
    5. 21.5 A Final Word
      1. Problems
  27. Chapter 22 - The Quest for Low Temperature
    1. 22.1 Cooling Off
    2. 22.2 The States of Matter
    3. 22.3 Behavior of Water
    4. 22.4 Liquefaction of Gases
    5. 22.5 The Joule-Thomson Effect
    6. 22.6 A Final Word
      1. Problems
  28. Appendix A - The International System of Units
  29. Appendix B - Conversion Factors
  30. Appendix C - Formulas From Algebra, Geometry, and Trigonometry
  31. Appendix D - Astronomical Data
  32. Appendix E - Physical Constants
  33. Selected Bibliography
  34. Index