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.
A more advanced course on classical dynamics, covering the Lagrangian and
be found here.
- 1. Newtonian Mechanics:
Introduction; Newton's Laws of Motion; Inertial Frames; Galilean Relativity; Newton's Second Law.
- 2. Forces:
Potentials in One Dimension; Equilibrium and Harmonic Oscillators; Central Forces; Angular Momentum; Gravity; Electromagnetsm; Friction.
- 3. Interlude: Dimensional Analysis:
Dimensions; Scaling and Bridgeman's Theorem.
- 4. Central Forces:
Polar Coordinates in the Plane; The Effective Potential; The Orbit Equation; The Kepler Problem and Kepler's Laws; Rutherford Scattering.
- 5. Systems of Particles:
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:
Newton's Laws in a Rotating Frame; Centrifugal Force; Coriolis Force; Foucaults Pendulum; Larmor Precession.
- 7. Special Relativity:
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 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
- 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