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Mechanics

Book Description

Mechanics meets the requirement for an ideal text on Mechanics for undergraduate students. The book gives the readers a better understanding of topics like Rectilinear Motion, Conservation of Energy and Equation of Motion, provides a good number of examples with good use of real-time illustrations and exercises for practice and challenge. The book comprehensively covers topics like Newton's Law of Motion, Conservation Laws of momentum, Energy and Law of Gravitation and includes 180 worked-out examples and 185 end-of-chapter exercises.

Table of Contents

  1. Cover
  2. Title Page
  3. Contents
  4. Dedication
  5. Preface
  6. 1 ■ Introduction
    1. 1.1 Mechanics, the Science of Motion
    2. 1.2 Time Evolution of Coordinates
    3. 1.3 Galileo’s Law of Inertia, Newton’s First Law of Motion
    4. 1.4 Experimental Verification of the First Law
    5. 1.5 Inertial Frame of Reference
    6. 1.6 In Search of Conservation Laws
    7. 1.7 Measure of Inertia, Inertial Mass
  7. 2 ■ Velocity and Acceleration in Rectilinear Motion
    1. 2.1 Displacement-Time Graph
    2. 2.2 Velocity of a Particle
    3. 2.3 Acceleration
    4. 2.4 Simple Harmonic Motion
    5. 2.5 Worked Out Examples I
    6. 2.6 Obtaining, T and X, Trelations from Areas of A-T and V-T Graphs
    7. 2.7 Standard Kinematical Relations for Constant Acceleration
    8. 2.8 Velocity and Displacement for a Harmonically Varying Acceleration
    9. 2.9 Worked Out Examples II
    10. ■ Summary
    11. ■ Exercises
  8. 3 ■ Vectors in Physics. Velocity and Acceleration as Vectors
    1. 3.1 Knowing Vectors by their Properties
    2. 3.2 Is Vector Just a Directed Straight Line?
    3. 3.3 Mathematical Representation of Vectors
    4. 3.4 The Displacement Vector
    5. 3.5 Magnitude of a Vector
    6. 3.6 Radius Vector as a Function of Time
    7. 3.7 The Velocity Vector
    8. 3.8 Infinitesimal Displacement, Line Element, Speed
    9. 3.9 Acceleration
    10. 3.10 Worked Out Examples I
    11. 3.11 Centripetal Acceleration in Uniform Circular Motion
    12. 3.12 Combination of Normal and Tangential Accelerations in Non-uniform Circular Motion
    13. 3.13 Worked Out Examples II
    14. 3.14 Multiplication of Two Vectors
    15. 3.15 Multiplication of Three Vectors
    16. 3.16 Worked Out Examples III
    17. ■ Summary
    18. ■ Exercises
  9. 4 ■ Conservation of Momentum
    1. 4.1 Galilean Transformation
    2. 4.2 Momentum in One Dimension. Definition of Mass
    3. 4.3 Conservation of Linear Momentum
    4. 4.4 Invariance of Momentum Conservation Under Galilean Transformation
    5. 4.5 Illustrative Examples of Momentum Conservation
    6. 4.6 Propulsion of a Rocket
    7. 4.7 Worked Out Examples. Set I
    8. 4.8 When There is a Flow of Momentum
    9. 4.9 Momentum Conservation from a Comoving Frame of Reference
    10. ■ Summary
    11. ■ Exercises
  10. 5 ■ Newton’s Second Law of Motion
    1. 5.1 How a Force Alters the Momentum of a Particle
    2. 5.2 Equations of Motion, and How to Solve Them
    3. 5.3 Can the Second Law be Applicable to Extended Objects?
    4. 5.4 Forces of Nature We Shall Reckon With
    5. 5.5 Motion Under Gravity Near the Surface of the Earth
    6. 5.6 Worked Out Examples. Set I
    7. 5.7 Motion Against Resistive Forces, Dry Friction
    8. 5.8 Worked Out Problems. Set II
    9. 5.9 Motion Against Resistive Forces, Fluid Friction
    10. 5.10 Worked Out Problems. Set III
    11. 5.11 Dynamics of a Spring Mass System
    12. 5.12 Worked Out Problems. Set IV
    13. 5.13 Simple Harmonic Motion in Two Perpendicular Directions, Lissajous Figures
    14. 5.14 The Second Law Applied to a System of Varying Mass
    15. 5.15 Worked Out Problems. Set V
    16. 5.16 Motion Under Electromagnetic Forces
    17. 5.17 Worked Out Problems. Set VI
    18. 5.18 The Second Law Applied to Uniform Circular Motion
    19. 5.19 Worked Out Examples. Set VII
    20. 5.20 Geometrical Structure of the Second Law Exemplified by Force Perpendicular to Velocity
    21. 5.21 Motion of a Charged Particle Moving in a Uniform Magnetic Field
    22. 5.22 Simple Pendulum
    23. ■ Summary
    24. ■ Exercises
  11. 6 ■ The Law of Universal Gravitation
    1. Part I: A Brief History of Gravitation
    2. 6.1 Newton and the Apple and the Moon
    3. 6.2 Heliocentric Model of Copernicus
    4. 6.3 Kepler’s Struggle with Mars
    5. 6.4 Kepler’s Third Law - Key to Inverse Square
    6. 6.5 The Law of Universal Gravitation
    7. Part II: Gravitational Field
    8. 6.6 The Gravitational Force Between Two Extended Objects
    9. 6.7 Gravitational Field
    10. 6.8 Direct Computation of the Gravitational Field
    11. 6.9 Satellites in Circular Orbits
    12. 6.10 Free Fall and Tidal Acceleration
    13. 6.11 Summary
    14. 6.12 Worked Out Problems
    15. 6.13 Appendix 6A: Explaining the Null Field Inside a Spherical Shell
    16. ■ Exercises
  12. 7 ■ Newton’s Third Law of Motion
    1. 7.1 A Slide Show on Newton's Third Law of Motion
    2. 7.2 Free Body Diagrams
    3. 7.3 Further Examples of FBDs
    4. 7.4 Every Real Force has a Parent
    5. 7.5 Worked Out Problems
    6. Exercises
  13. 8 ■ Work and Energy in One Dimensional Motion
    1. 8.1 Work and Kinetic Energy
    2. 8.2 Example of Work – Work Done by the Uniform Force of Gravity – Near the Earth’s Surface
    3. 8.3 Example of Work – Work Done by the Inverse Square Force of Gravity
    4. 8.4 Power – The Rate of Doing Work
    5. 8.5 Example of Work – The Spring Mass System
    6. 8.6 Example of Work – Work Done by Electrostatic Forces
    7. 8.7 Conservative and Non-Conservative Forces
    8. 8.8 The Concept of Potential Energy – Example Spring
    9. 8.9 Potential Energy in General
    10. 8.10 Total Energy of a Particle in a Conservative Field
    11. 8.11 Energy Conservation in a Spring Mass System
    12. 8.12 Concept of a Potential Well
    13. 8.13 Energy Conservation of a Particle Freely Falling Under the Gravitational Pull of the Earth (or the Sun)
    14. 8.14 Energy Conservation of a Charged Particle Moving in an Electrostatic Field
    15. 8.15 Work and Energy in Rocket Propulsion
    16. 8.16 Summary of Important Formulas
    17. 8.17 Worked Out Problems
    18. ■ Exercises
  14. 9 ■ Motion Under Central Forces
    1. 9.1 Plane Polar Co-ordinate System
    2. 9.2 Velocity and Acceleration of a Particle in the Polar System
    3. 9.3 Orbital Angular Momentum
    4. 9.4 Equations of Motion in the Polar Coordinate System
    5. 9.5 Motion Under an Inverse-Square-Law Attractive Force
    6. 9.6 Classification of Trajectories in an Inverse-Square-Law Field – Kepler’s 1st Law of Planetary Orbit
    7. 9.7 Kepler’s Third Law of Planetary Orbits
    8. 9.8 A Closer Look at Planetary (Satellite) Orbits
    9. 9.9 The Parabolic Trajectory of a Projectile is Part of an Elliptical Orbit
    10. 9.10 Motion Under an Inverse-Square-Law Repulsive Force
    11. 9.11 Appendix 9A: Conic Sections – Ellipse, Parabola, Hyperbola
    12. 9.12 Summary
    13. 9.13 Worked Out Problems
    14. ■ Exercises
  15. 10 ■ Work and Energy in 3-Dimensional Motion
    1. 10.1 Normal and Tangential Accelerations
    2. 10.2 Effect of Force Acting Over a Displacement – General Case
    3. 10.3 Evaluation of the Line Integral
    4. 10.4 Example of Evaluation of W – Work Done by the Force of Gravity
    5. 10.5 Example of Evaluation of W – Work Done by the Induced Electric Force
    6. 10.6 Relationship of Work to Kinetic Energy
    7. 10.7 Potential Energy of a Particle in a Conservative Field
    8. 10.8 Total Energy of a Particle in a Conservative Field
    9. 10.9 How Energy Determines the Forces of Constraint
    10. 10.10 The Example of a Betatron
    11. 10.11 Appendix 10A: How to Calculate the Radius of Curvature
    12. 10.12 Summary of Important Formulas
    13. 10.13 Worked Out Problems
    14. ■ Exercises
  16. 11 ■ Ideal Fluid at Rest and in Motion
    1. 11.1 Stresses Inside a Fluid
    2. 11.2 Hydrostatic Pressure Equation
    3. 11.3 Hydrostatic Devices
    4. 11.4 Archimedes’ Principle
    5. 11.5 Worked Out Examples. Set I
    6. 11.6 Elementary Mechanics of Fluid Flow
    7. 11.7 Poiseulle’s Law
    8. 11.8 Summary of Important Formulas
    9. 11.9 Worked Out Examples. Set II
    10. ■ Exercises
  17. 12 ■ Motion of a System of Particles. Rigid Body Rotating about a Fixed Axis
    1. 12.1 Linear Bulk Motion of a System of Particles – Conservation of Momentum
    2. 12.2 Rotational Motion of a System of Particles – Conservation of Angular Momentum
    3. 12.3 Examples of Centre of Mass. Worked Out examples I
    4. 12.4 Worked Out Examples II
    5. 12.5 Breaking Up Dynamical Variables With a Component in the CM Frame
    6. 12.6 Rotation of a Rigid Body About a Fixed Axis
    7. 12.7 Simplest Examples of Rigid Body Dynamics
    8. 12.8 Angular Momentum is a Vector Quantity
    9. 12.9 The Amazing Gyroscope, the Spinning Top
    10. 12.10 The 2-Body Problem
    11. 12.11 Collision of Two Particles
    12. ■ Summary
    13. ■ Exercises
  18. 13 ■ Accelerating and Rotating Frames of Reference
    1. 13.1 Linearly Accelerating Frame of Reference
    2. 13.2 Rotating Frame of Reference
    3. 13.3 Pseudo Forces Near the Earth’s Surface
    4. 13.4 Principle of Equivalence, Inertial Force and Pseudo-Gravity
    5. 13.5 Worked Out Problems
    6. ■ Summary
    7. ■ Exercises
  19. 14 ■ Relativistic Mechanics
    1. 14.1 Event Point in Space-Time
    2. 14.2 Historical Background
    3. 14.3 The Postulates of Relativity and Consequences
    4. 14.4 Worked Out Examples I
    5. 14.5 Relativistic Mechanics
    6. 14.6 Worked Out Examples II
    7. ■ Summary
    8. ■ Exercises
  20. Appendix A ■ Beam Bending and Deflection Formulas
    1. A.1 Why Should a Beam Bend?
    2. A.2 Hook’s Law
    3. A.3 Bending Moment
    4. A.4 The Flexure Formula
    5. A.5 Deflection of Beams
    6. A.6 Conclusion
  21. Appendix B ■ Instructions for Gnuplot
    1. B.1 To Start With
    2. B.2 Example 1: The Parabolic Trajectory of a Projectile
    3. B.3 Example 2: Gun Intercepting a Bomb
    4. B.4 Example 3: Displacement, Velocity and Acceleration of a Piston Driven by a Crank Wheel
    5. B.5 Example 4: Plotting Polar Equations of Conic Sections
    6. B.6 Example 5: Processing Ellipse
    7. B.7 Example 6: Plotting the G-Path of Mars
    8. B.8 Example 7: Lissajous Figures
  22. Notes
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 5
    5. Chapter 6
    6. Chapter 7
    7. Chapter 8
    8. Chapter 9
    9. Chapter 10
    10. Chapter 11
    11. Chapter 12
    12. Chapter 13
    13. Chapter 14
  23. Bibliography
  24. Acknowledgements
  25. Copyright