Free lessons, worked step by step

Clear lessons on the topics students get stuck on, each with a worked example, the mistakes people make, a quick check, and an interactive simulation where it helps. Free, no sign-in needed.

Engineering

Beam support reactionsHow to find the support reactions of a simply supported beam with point loads and distributed loads, step by step, with an interactive beam.First-year engineering · 10 min · simulation · 3 diagramsStart lesson
Shear force and bending moment diagramsHow to draw shear force and bending moment diagrams for a simply supported beam, with the rules that make them quick and an interactive example.First- and second-year engineering · 12 min · simulation · 3 diagramsStart lesson
Trusses: the method of jointsHow to find the force in every member of a truss using the method of joints, with tension and compression explained and an interactive truss.First-year engineering · 12 min · simulation · 2 diagramsStart lesson
Torsion in circular shaftsHow torque twists a circular shaft: the torsion formula for shear stress, the polar moment of area, and the angle of twist, with a worked example.Second-year engineering · 10 min · simulation · 3 diagramsStart lesson
Stress and strainWhat stress and strain are, how Young's modulus links them, and how to find how much a loaded rod stretches, with a worked example.Senior school and first-year engineering · 8 min · simulation · 3 diagramsStart lesson
Bernoulli's equationWhat Bernoulli's equation says about pressure, velocity and height in a flowing fluid, when you can use it, and a worked example with a narrowing pipe.Senior school and first-year engineering · 10 min · 2 diagramsStart lesson
The Carnot cycle and heat engine efficiencyWhy no heat engine can be 100% efficient, how the Carnot efficiency sets the limit, and how to use it to check whether an engine claim is possible.Senior school and first-year engineering · 8 min · 2 diagramsStart lesson
The vapour-compression refrigeration cycleHow fridges and air conditioners move heat using the vapour-compression cycle, what COP means, and how to calculate it from refrigerant enthalpies.Second- and third-year engineering · 12 min · 2 diagramsStart lesson
Present worth and the time value of moneyWhy money now is worth more than money later, how to discount a future amount or a series of payments to present worth, and how engineers compare projects.Engineering economics · 10 min · 2 diagramsStart lesson
Beam deflectionCalculate cantilever tip deflection using load, span, elastic modulus and second moment of area, with worked examples.First-year engineering · 10 min · simulation · 2 diagramsStart lesson
Bending stress in beamsUse the flexure formula to find beam bending stress, identify the neutral axis and locate maximum tension and compression.First-year engineering · 10 min · 2 diagramsStart lesson
Centroids and second moment of areaFind composite-area centroids and second moments of area with the rectangle formula and parallel-axis theorem.First-year engineering · 10 min · simulation · 2 diagramsStart lesson
Column buckling and Euler's formulaCalculate Euler buckling loads, choose effective-length factors, and learn when elastic column buckling governs.Second-year university engineering · 10 min · simulation · 2 diagramsStart lesson
The first law of thermodynamicsUnderstand energy conservation, heat and work sign conventions, and piston boundary-work calculations for closed systems.Second-year university engineering · 10 min · 2 diagramsStart lesson
Free body diagramsLearn to draw free body diagrams, resolve forces and apply Newton’s second law to equilibrium and acceleration problems.First-year engineering · 10 min · simulation · 2 diagramsStart lesson
Heat conduction through wallsCalculate steady heat flow through walls using Fourier law, temperature differences and thermal resistances.Second-year university engineering · 10 min · 2 diagramsStart lesson
Hydrostatic pressure and buoyancyLearn pressure at depth, gauge and absolute pressure, Archimedes principle, and buoyancy force calculations.Second-year university engineering · 10 min · 2 diagramsStart lesson
Mohr's circle for plane stressLearn how to draw Mohr's circle, find principal and maximum shear stresses, and check plane-stress transformations.Second-year university engineering · 10 min · simulation · 2 diagramsStart lesson

Physics

Chemistry

Moles and stoichiometryConvert between mass, moles and particles, use balanced equations, and identify the limiting reactant in chemical calculations.Senior school chemistry · 10 min · 2 diagramsStart lesson

Mathematics

Statistics

Economics