David Tong: Lectures on Dynamics and Relativity

This is an introductory course on Newtonian mechanics and special relativity given to first year undergraduates. The notes were last updated in April 2012. Individual chapters and problem sheets are available below. The full set of lecture notes come in around 145 pages and can be downloaded here. Please do email me if you find any typos or corrections.

PostScript      PDF

A more advanced course on classical dynamics, covering the Lagrangian and Hamiltonian formulations, can be found here.

Content

• 1. Newtonian Mechanics:   Postscript    PDF
  Introduction; Newton's Laws of Motion; Inertial Frames; Galilean Relativity; Newton's Second Law
• 2. Forces:   Postscript    PDF
  Potentials in One Dimension; Equilibrium and Harmonic Oscillators; Central Forces; Angular Momentum; Gravity; Electromagnetsm; Friction.
• 3. Interlude: Dimensional Analysis:   Postscript    PDF
  Dimensions; Scaling and Bridgeman's Theorem.
• 4. Systems of Particles:   Postscript    PDF
  Centre of Mass Motion; Two Body Problem; Collisions; Variable Mass Problems.
• 5. Central Forces:   Postscript    PDF
  Polar Coordinates in the Plane; The Effective Potential; The Orbit Equation; The Kepler Problem and Kepler's Laws; Rutherford Scattering.
• 6. Rigid Bodies:   Postscript    PDF
  Angular Velocity; Moments of Inertia; Parallel Axis Theorem; Motion of Rigid Bodies; Rolling, Rolling, Rolling.
• 7. Non-Inertial Frames:   Postscript    PDF
  Newton's Laws in a Rotating Frame; Centrifugal Force; Coriolis Force.
• 8. Special Relativity:   Postscript    PDF
  Lorentz Transformations; Spacetime Diagrams; Simultaneity; Causality; Time Dilation; Length Contraction; Addition of Velocities; The Geometry of Spacetime; The Lorentz Group; Kinematics; Particle Physics

Problem Sheets

• Problem Sheet 1:   Postscript    PDF    Single Particle Mechanics


• Problem Sheet 2:   Postscript    PDF    Systems of Particles and Central Forces


• Problem Sheet 3:   Postscript    PDF    Orbits and Other Spinning Things


• Problem Sheet 4:   Postscript    PDF    Special Relativity

Classical Mechanics on the Web

• Last Year's Course by Stephen Siklos, Cambridge   


• Mechanics:   by Daniel Arovas, UCSD


• Mechanics and Special Relativity:   by Howard Georgi, Harvard


• Special Relativity:   by Gary Gibbons, Cambridge. (Directly downloads pdf file).


• Special Relativity:   by Joe Minahan, Uppsala.

Some Classic Resources

• Newton's Papers    recently digitised by Cambridge University


• The Special and General Theory of Relativity    by Albert Einstein


• Gravitational Wells    by xkcd.