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 March 2013. Individual chapters and problem sheets are available below. The full set of lecture notes come in around 160 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:   PDF
  Introduction; Newton's Laws of Motion; Inertial Frames; Galilean Relativity; Newton's Second Law.
• 2. Forces:   PDF
  Potentials in One Dimension; Equilibrium and Harmonic Oscillators; Central Forces; Angular Momentum; Gravity; Electromagnetsm; Friction.
• 3. Interlude: Dimensional Analysis:   PDF
  Dimensions; Scaling and Bridgeman's Theorem.
• 4. Central Forces:   PDF
  Polar Coordinates in the Plane; The Effective Potential; The Orbit Equation; The Kepler Problem and Kepler's Laws; Rutherford Scattering.
• 5. Systems of Particles:   PDF
  Centre of Mass Motion; Two Body Problem; Collisions; Variable Mass Problems; Rigid Bodies; Angular Velocity; Moments of Inertia; Parallel Axis Theorem; Motion of Rigid Bodies; Rolling, Rolling, Rolling.
• 6. Non-Inertial Frames:   PDF
  Newton's Laws in a Rotating Frame; Centrifugal Force; Coriolis Force; Foucaults Pendulum; Larmor Precession.
• 7. Special Relativity:   PDF
  Lorentz Transformations; Spacetime Diagrams; Simultaneity; Causality; Time Dilation; Length Contraction; Addition of Velocities; The Geometry of Spacetime; The Lorentz Group; Kinematics; Particle Physics; The Lorentz Group as SL(2,C); Terrell-Penrose Rotations; Spinors.

Problem Sheets

• Problem Sheet 1:   Postscript    PDF    Single Particle Mechanics


• Problem Sheet 2:   Postscript    PDF    Central Forces and Orbits


• Problem Sheet 3:   Postscript    PDF    Systems of Particles and Spinning Things


• Problem Sheet 4:   Postscript    PDF    Special Relativity

Classical Mechanics on the Web

• Dynamics and Relativity by Stephen Siklos, Cambridge   


• Mechanics:   by Daniel Arovas, UCSD


• 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


• What Would Newton Do?    A lecture on the geometrical proofs used in the Principia.