Mathematical Review & Physical World
Build the mathematical language used throughout physics: relationships, graphs, rates and accumulation.
GraphsTrigonometryCalculus
Physics chapters
Work through four volumes in order, or return to a section you need. Fluids keeps its two-part layout; maths, vectors and friction remain separate coaching modules.
Volume 1 · Foundations & Motion
Units and Measurements
Learn how to report a measurement, check an equation and propagate uncertainty.
DimensionsMeasurement errorsInstruments
Motion in a Straight Line
Separate position, displacement and distance; connect graphs with equations; then handle relative motion, gravity and changes of direction..
Motion graphsFree fallRelative motion
Vectors
Understand direction before using projectile, force or torque equations.
ComponentsDot productCross product
Motion in a Plane
Resolve two-dimensional motion into perpendicular directions, then connect projectiles, relative velocity and circular motion..
ProjectilesRiver crossingsCircular motion
Laws of Motion · Part 1
Use free-body diagrams to connect forces with changes in momentum.
Free-body diagramsConnected massesMomentum
Volume 2 · Forces, Energy & Rotation
Laws of Motion · Part 2: Friction
Friction responds to the tendency to slip.
Static frictionInclinesConnected bodies
Work, Energy & Power
Use work to track energy changes, recognise conservative forces and analyse collisions.
Work–energy theoremCollisionsPower
System of Particles & Rotational Motion
Track the centre of mass, then distinguish translation from rotation.
Centre of massMoment of inertiaRolling
Volume 3 · Gravity, Materials & Oscillations
Gravitation
Connect force, field and potential, then derive orbital motion and escape speed.
Gravity & potentialSatellitesEscape speed
Mechanical Properties of Solids
Stress, strain, Hooke's law, the stress–strain curve, Young's, shear and bulk moduli, Poisson's ratio, elastic energy, combined wires, own weight, thermal stress and applications.
Wire labStress–strain curveBeam bending
Fluids I: Pressure to Bernoulli
Pressure and depth, atmospheric and gauge pressure, Pascal's law, buoyancy, continuity, Bernoulli, Torricelli, venturimeter, dynamic lift, Magnus effect and accelerating containers.
Hydraulic liftFloating labWater jets
Fluids II: Viscosity & Surface Tension
Viscosity, Stokes' law, terminal velocity, Reynolds number, surface tension and energy, angle of contact, drops and bubbles, capillary rise and its surface-tension experiment, plus viscous pipe flow.
Terminal velocityBubblesCapillary tube
Oscillations
Start with restoring forces and phase, then connect displacement, velocity and energy.
SHMSprings & pendulumsResonance
Volume 4 · Waves & Thermal Physics
Waves
Follow a disturbance travelling through a medium while its particles oscillate locally.
Standing wavesBeatsDoppler effect
Thermal Properties of Matter
Separate temperature from heat, then explain expansion, calorimetry, phase changes and heat transfer.
ExpansionCalorimetryHeat transfer
Kinetic Theory of Gases
Connect random molecular motion to pressure and temperature.
Molecular speedsHeat capacitiesMean free path
Thermodynamics
Account for heat, work and internal energy with one consistent sign convention.
Gas processesHeat enginesCarnot cycle