The principles of classical physics, though superseded in specific fields by such theories as quantum mechanics and general relativity, are still of great importance in a broad range of applications. The book presents fundamental concepts of classical physics in a coherent and logical manner. It discusses important topics including the mechanics of a single particle, kinetic theory, oscillations and waves. Topics including the kinetic theory of gases, thermodynamics and statistical mechanics are discussed, which are normally not present in the books on classical physics. The fundamental concepts of energy, momentum, mass and entropy are explained with examples. Discussion on concepts of thermodynamics is presented along with the simplified explanation on Caratheodory's axioms. It covers chapters on wave motion and statistical physics, useful for the graduate students. Each concept is supported with real-life applications on several concepts including impulse and collision, Bernoulli's equation, and friction.
Author(s): Sudhir Ranjan Jain
Series: Cambridge IISc Series
Publisher: Cambridge University Press
Year: 2016
Language: English
Pages: 231
Contents......Page 7
Figures......Page 13
Preface......Page 18
Acknowledgments......Page 20
1.1 Energy......Page 22
1.1.1 Car driving......Page 24
1.2 Mass......Page 25
1.3 Momentum......Page 28
2.1 Whether to Stop or Run Through?......Page 31
2.2 Vertical Jump......Page 34
2.2.1 Height equation: from conservation law......Page 35
2.2.2 Jumps of animals......Page 36
2.3 Hourglass......Page 37
2.4 Motion of a Chain in a Tube......Page 38
2.5.1 Gravitation......Page 40
2.5.3 Strong interaction......Page 42
3.1 Cartesian vs Polar Coordinates......Page 44
3.2 Coriolis Force......Page 48
3.3 Rotation Group......Page 49
4.1.1 Mechanics......Page 50
4.1.2 Electric circuits......Page 51
4.1.3 Optics......Page 52
4.2 The Principle of Least Action......Page 53
4.3 More Thoughts on Why “(T −V )”?......Page 55
5 Work and Energy......Page 56
5.1 At the T-junction......Page 57
5.2 Motion of a Heavy Particle on a Smooth Curve in a Vertical Plane......Page 60
5.3 Motion of a Heavy Particle, Placed on the Outside of a Smooth Circle in a Vertical Plane and Allowed to Slide Down......Page 61
5.4 Motion in a Vertical Plane of a Heavy Particle Attached by a Fine String to a Fixed Point......Page 62
5.5 Conservative Force......Page 63
5.5.1 Interpretation of grad V......Page 64
5.6.1 Galilean invariant......Page 65
5.6.2 Example......Page 67
6 Mechanics of a System of Particles......Page 69
6.1.1 Simple ‘usual’ pendulum......Page 70
6.1.2 Leaking bob......Page 71
6.2 Work-energy Theorem Revisited......Page 74
6.3 Displacement......Page 76
6.4 Rotation......Page 77
6.5 Rigid Body Motion: Basic Ideas......Page 78
6.6 Rotation of a Rigid Body about an Arbitrary Axis......Page 81
6.6.1 Special cases......Page 82
6.7 Moments of Inertia of Simple Bodies......Page 83
6.8 Principal Axes — Stationary Points of Kinetic Energy......Page 85
6.9 Euler’s Equations......Page 87
7.1 Non-conservative Forces and Energy Loss......Page 91
7.1.1 Energy loss......Page 92
7.2 Bowling — Physics of the Rolling Ball......Page 93
7.3 Squealing and Squeaking......Page 98
8.1.1 Direct impact......Page 99
8.1.2 Poisson’s hypothesis......Page 100
8.1.3 Kinetic energy lost by impact......Page 101
8.1.4 Generalization of Newton’s rule......Page 102
8.2.1 Deformation energy......Page 103
8.2.2 Impact force......Page 104
8.3 Falling Pencil on a Table......Page 107
9.1 The Two-body Problem......Page 112
9.1.1 Bounded orbits......Page 115
9.2.1 Case I......Page 117
9.2.2 Case II......Page 118
9.3 Satellite Paradox......Page 119
9.3.1 Descending path on a near-circular orbit......Page 120
9.4 Rotation Curves: an Anomaly......Page 122
9.5 The Rosetta-Philae Comet Mission......Page 123
10.1 Black Holes at LHC......Page 125
10.2 Nuclear Explosion......Page 126
10.3 Insect Flight......Page 127
11.1 Free Oscillations......Page 129
11.3 Compound Pendulum......Page 130
11.4 Damped Harmonic Oscillator......Page 131
11.5 Driven Damped Simple Harmonic Oscillator......Page 132
11.7 Another Instance of Simple Harmonic Motion......Page 135
11.8 Two Coupled Oscillators......Page 137
11.9 Three Coupled Oscillators......Page 140
11.10 Many Coupled Oscillators......Page 141
11.11 Dissipation by a Rapidly Oscillating Potential......Page 143
12.1 Transverse Modes of a String......Page 145
12.2.1 Reflection and transmission of waves on a string......Page 147
12.3 Standing Waves on Planar Membranes......Page 149
12.4.1 Newton’s derivation......Page 152
12.4.2 Correct derivation (Laplace)......Page 154
13.1 Physics of Music......Page 157
13.2 Western Classical Music......Page 160
13.3 Transposition, Musical Scales, and Algebraic Groups......Page 161
14 Fluid Mechanics......Page 163
14.2 Euler’s Equation......Page 165
14.2.1 Applications......Page 166
14.4 Streamlines......Page 167
14.5 Speed of Sound Inside a Fluid......Page 168
14.5.1 Effect of bubbles......Page 169
14.6 Sound of a Brook......Page 171
14.7 Why is Water Watery?......Page 172
15.1 Gravity Waves in Liquid......Page 174
15.1.2 Shallow water waves (Tsunami)......Page 176
15.2 Capillary Waves......Page 177
16 The Kinetic Theory of Gases......Page 180
16.1 Equipartition of Kinetic Energy, Ideal Gas Law......Page 181
16.2 Football Game: Kinetic Theory Perspective......Page 183
16.3 Adiabatic Reversible Compression......Page 185
16.4 Adiabatic Reversible Compression (from Mechanics and Kinetic Theory)......Page 186
17 Concepts and Laws of Thermodynamics......Page 188
17.1 Adiabatic Transitions and Accessibility of States of a System - Empirical Entropy, First and Second Laws......Page 189
17.2 Sears’ Illustration of Caratheodory’s Treatment......Page 191
17.3.1 Reversible process......Page 195
17.3.3 Irreversibility......Page 196
17.4 Order or Disorder......Page 197
17.5 How Does Entropy Look Like?......Page 198
18.1 Thermodynamic Potentials......Page 202
18.2 Van der Waals Equation for Real Gases......Page 205
18.2.1 Liquefaction of gases......Page 206
18.3 The Third Law of Thermodynamics......Page 207
18.4.1 Diffusion......Page 208
18.4.2 Law of mass action......Page 210
18.5 Chemical Potential......Page 211
18.6 Van’t Hoff Equation of State for Dilute Solutions......Page 213
19.1 Gibbs and Boltzmann Entropies......Page 215
19.2 Boltzmann Factor: Application to “Phases of Matter”......Page 218
19.2.1 Gases and solids......Page 219
19.2.2 Liquids......Page 221
19.3 Failure of Classical Physics......Page 222
Bibliography......Page 224
Index......Page 230
