Dynamics and relativity

A new title in the Manchester Physics Series, this introductory text emphasises physical principles behind classical mechanics and relativity. It assumes little in the way of prior knowledge, introducing relevant mathematics and carefully developing it within a physics context. Designed to provide a logical development of the subject, the book is divided into four sections, introductory material on dynamics, and special relativity, which is then followed by more advanced coverage of dynamics and special relativity. Each chapter includes problems ranging in difficulty from simple to challenging with solutions for solving problems. Includes solutions for solving problems Numerous worked examples included throughout the book Mathematics is carefully explained and developed within a physics environment Sensitive to topics that can appear daunting or confusing

Author Notes

Dr Jeff Forshaw , Department of Physics & Astronomy, University of Manchester, Oxford Road, Manchester, UK.

Dr Gavin Smith , Department of Physics & Astronomy, University of Manchester, Oxford Road, Manchester, UK.

Reviews 1

Choice Review

Dynamics and Relativity is a very readable, pedagogically effective undergraduate resource that prepares students well for more advanced graduate-level classical mechanics courses. Forshaw and Smith (both, Univ. of Manchester, UK) carefully treat conventional classical mechanics topics with interesting examples, and provide helpful guidance through some of the more difficult derivations and concepts. Modern applications and the general physical implications of the equations and results appear throughout the text. The authors introduce vector notation on p. 5 and use this notation consistently and very effectively in the book. The careful consideration of frames of reference and coordinate systems and the distinction between inertial and accelerating reference frames are made early on and ease the development of special relativity that is the subject of the last third of the book. The book is less detailed than standard mechanics works such as H. Goldstein's Classical Mechanics (3rd ed., 2002) and K. Symon's Mechanics (3rd ed., 1971). The former provides preparation for quantum mechanics, while the latter contains extensive examples, problems, and detailed calculations and would be a useful companion to the current work. The authors' systematic and thoughtful approach is effective for a first course. Minimal references and footnotes. Summing Up: Recommended. Upper-division undergraduate through professional collections. M. Coplan Institute for Physical Science and Technology

Editors' Preface to the Manchester Physics Series	p. xi
Author's Preface	p. xiii
I Introductory Dynamics	p. 1
1 Space, Time and Motion	p. 3
1.1 Defining Space and Time	p. 3
1.1.1 Space and the classical particle	p. 4
1.1.2 Unit vectors	p. 6
1.1.3 Addition and subtraction of vectors	p. 6
1.1.4 Multiplication of vectors	p. 7
1.1.5 Time	p. 8
1.1.6 Absolute space and space-time	p. 10
1.2 Vectors and Co-ordinate Systems	p. 11
1.3 Velocity and Acceleration	p. 14
1.3.1 Frames of reference	p. 16
1.3.2 Relative motion	p. 16
1.3.3 Uniform acceleration	p. 18
1.3.4 Velocity and acceleration in plane-polar co-ordinates: uniform circular motion	p. 20
1.4 Standards and Units	p. 21
2 Force, Momentum and Newton's Laws	p. 25
2.1 Force and Static Equilibrium	p. 25
2.2 Force and Motion	p. 31
2.2.1 Newton's Third Law	p. 35
2.2.2 Newton's bucket and Mach's principle	p. 39
2.3 Applications of Newton's Laws	p. 41
2.3.1 Free body diagrams	p. 41
2.3.2 Three worked examples	p. 42
2.3.3 Normal forces and friction	p. 46
2.3.4 Momentum conservation	p. 49
2.3.5 Impulse	p. 51
2.3.6 Motion in fluids	p. 51
3 Energy	p. 55
3.1 Work, Power and Kinetic Energy	p. 56
3.2 Potential Energy	p. 61
3.2.1 The stability of mechanical systems	p. 64
3.2.2 The harmonic oscillator	p. 65
3.2.3 Motion about a point of stable equilibrium	p. 67
3.3 Collisions	p. 68
3.3.1 Zero-momentum frames	p. 68
3.3.2 Elastic and inelastic collisions	p. 71
3.4 Energy Conservation in Complex Systems	p. 75
4 Angular Momentum	p. 81
4.1 Angular Momentum of a Particle	p. 81
4.2 Conservation of Angular Momentum in Systems of Particles	p. 83
4.3 Angular Momentum and Rotation About a Fixed Axis	p. 86
4.3.1 The parallel-axis theorem	p. 94
4.4 Sliding and Rolling	p. 95
4.5 Angular Impulse and the Centre of Percussion	p. 97
4.6 Kinetic Energy of Rotation	p. 99
II Introductory Special Relativity	p. 103
5 The Need for a New Theory of Space and Time	p. 105
5.1 Space and Time Revisited	p. 105
5.2 Experimental Evidence	p. 108
5.2.1 The Michelson-Morley experiment	p. 108
5.2.2 Stellar aberration	p. 110
5.3 Einstein's Postulates	p. 113
6 Relativistic Kinematics	p. 115
6.1 Time Dilation, Length Contraction and Simultaneity	p. 115
6.1.1 Time dilation and the Doppler effect	p. 116
6.1.2 Length contraction	p. 121
6.1.3 Simultaneity	p. 123
6.2 Lorentz Transformations	p. 124
6.3 Velocity Transformations	p. 129
6.3.1 Addition of velocities	p. 129
6.3.2 Stellar aberration revisited	p. 130
7 Relativistic Energy and Momentum	p. 135
7.1 Momentum and Energy	p. 135
7.1.1 The equivalence of mass and energy	p. 142
7.1.2 The hint of an underlying symmetry	p. 144
7.2 Applications in Particle Physics	p. 145
7.2.1 When is relativity important?	p. 146
7.2.2 Two useful relations and massless particles	p. 149
7.2.3 Compton scattering	p. 152
III Advanced Dynamics	p. 157
8 Non-Inertial Frames	p. 159
8.1 Linearly Accelerating Frames	p. 159
8.2 Rotating Frames	p. 161
8.2.1 Motion on the earth	p. 165
9 Gravitation	p. 173
9.1 Newton's Law of Gravity	p. 174
9.2 The Gravitational Potential	p. 177
9.3 Reduced Mass	p. 182
9.4 Motion in a Central Force	p. 184
9.5 Orbits	p. 186
10 Rigid Body Motion	p. 197
10.1 The Angular Momentum of a Rigid Body	p. 198
10.2 The Moment of Inertia Tensor	p. 200
10.2.1 Calculating the moment of inertia tensor	p. 203
10.3 Principal Axes	p. 207
10.4 Fixed-axis Rotation in the Lab Frame	p. 212
10.5 Euler's Equations	p. 214
10.6 The Free Rotation of a Symmetric Top	p. 216
10.6.1 The body-fixed frame	p. 216
10.6.2 The lab frame	p. 218
10.6.3 The wobbling earth	p. 223
10.7 The Stability of Free Rotation	p. 224
10.8 Gyroscopes	p. 226
10.8.1 Gyroscopic precession	p. 226
10.8.2 Nutation of a gyroscope	p. 232
IV Advanced Special Relativity	p. 237
11 The Symmetries of Space and Time	p. 239
11.1 Symmetry in Physics	p. 239
11.1.1 Rotations and translations	p. 240
11.1.2 Translational symmetry	p. 245
11.1.3 Galilean symmetry	p. 246
11.2 Lorentz Symmetry	p. 247
12 Four-Vectors and Lorentz Invariants	p. 253
12.1 The Velocity Four-vector	p. 254
12.2 The Wave Four-vector	p. 255
12.3 The Energy-momentum Four-vector	p. 258
12.3.1 Further examples in relativistic kinematics	p. 259
12.4 Electric and Magnetic Fields	p. 262
13 Space-Time Diagrams and Causality	p. 267
13.1 Relativity Preserves Causality	p. 270
13.2 An Alternative Approach	p. 272
14 Acceleration and General Relativity	p. 279
14.1 Acceleration in Special Relativity	p. 279
14.1.1 Twins paradox	p. 280
14.1.2 Accelerating frames of reference	p. 282
14.2 A Glimpse of General Relativity	p. 288
14.2.1 Gravitational fields	p. 290
A Deriving the Geodesic Equation	p. 295
B Solutions to Problems	p. 297

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