Dynamics and Relativity
This is an introductory course on Newtonian mechanics and special relativity, given to first year undergraduates. Individual chapters and problem sheets are available below. The full set of lecture notes come in around 160 pages.
If you enjoy the notes, an extended version is available as a textbook.
Newtonian Mechanics
Introduction; Newton’s Laws of Motion; Inertial Frames; Galilean Relativity; Newton’s Second Law.
Forces
Potentials in One Dimension; Equilibrium and Harmonic Oscillators; Central Forces; Angular Momentum; Gravity; Electromagnetism; Friction.
Interlude: Dimensional Analysis
Dimensions; Scaling and Bridgman’s Theorem.
Central Forces
Polar Coordinates in the Plane; The Effective Potential; The Orbit Equation; The Kepler Problem and Kepler’s Laws; Rutherford Scattering.
Systems of Particles
Centre of Mass Motion; Two Body Problem; Collisions; Variable Mass Problems; Rigid Bodies; Moments of Inertia; Parallel Axis Theorem; Motion of Rigid Bodies; Rolling, Rolling, Rolling.
Non-Inertial Frames
Newton’s Laws in a Rotating Frame; Centrifugal Force; Coriolis Force; Foucault’s Pendulum; Larmor Precession.
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.