Physics: 104 lessons, each with a live simulation

Every tool on this shelf

Mechanics & Motion

Oscillations, Waves & Optics

Thermodynamics

Electricity, Magnetism & Circuits

Control Systems & Modern Physics

Other tools

Chapters

Mechanics

L2: school

Energy instead of forces

PHYTwo tools and one shortcut: when all you want is speeds and heights, you can skip the forces entirely and let energy keep the books.

L2: school

Newton's laws: the grip a motion asks for

PHYEvery mechanics problem with a surface in it has to settle one question before any arithmetic: how much friction does this motion need, and can the contact give it? A block on a plank answers with tan θ against μ. A car on a banked bend adds a turn, and the friction it needs changes direction with the speed. A ball rolling down a ramp adds a spin, and the hoop, which asks for the most grip, is the first to slip.

L2: school

Simple machines: trading force for distance

PHYFive machines and one bargain. None of them creates energy, and every one of them lets you choose how to spend it: a smaller force over a longer path, or the reverse. Each step hands the next a specific piece of that bargain, and by the end you can read any machine by asking two questions about it.

L2: school

Throwing things

PHYThree tools, and the third one breaks the first two. Constant acceleration has a closed-form answer, so the first two steps are algebra. Air resistance is not constant, and from there the only honest method is to integrate it step by step.

L2: school

Least time, least action

PHYThe path a light ray takes, a sliding bead follows and a thrown ball flies is the one along which a small change makes no first-order change in a total: time for the first two, action for the ball. Every page lets you bend the path and watch the total barely move, and two of them find a path whose total is stationary without being least.

L2: school

Rotation and angular momentum

PHYA spinning body carries a vector, its angular momentum, and nearly everything surprising about rotation is that vector refusing to change. Pull your arms in on a turntable and you spin faster; a wheel turns sideways instead of falling; a racket flips; a pendulum's plane stays put while the floor turns under it.

L3: undergraduate

Where the load goes

PHYSeven pages on one question: which part of a structure is actually carrying the weight, and in what form. It starts inside a single beam, where the middle does almost nothing, and ends with a truss that has more bars than equations and still says exactly when it will fall.

Fluids

L2: school

Water out of a tank: one speed, spent two ways

PHYTwo tools built on a single result. Water leaves a hole at exactly the speed a stone reaches falling the same depth, and everything else follows from where that speed is spent: sideways it is a projectile, downwards it is the tank emptying itself.

L2: school

Fluids at rest: from a pressure gauge to a mountain's root

PHYPressure in a still liquid depends on the depth and on nothing else: not the area, not the amount of liquid, not the shape of the vessel. Apply that to the top and the bottom of a body and you have the upthrust. Floating then has a single rule, that a floating body pushes aside its own mass of liquid, and the rule does not care whether the body is a rowing boat on a pond or a continent on the mantle.

L2: school

Fluids in motion: what viscosity takes back

PHYBernoulli's pipe has no friction in it, and each page after it puts back something that one left out. Viscosity costs pressure along a pipe. The Reynolds number decides whether that cost is the orderly one Poiseuille computed. A sinking grain shows the same number choosing between two drag laws, and in the band between them, where no formula holds, the last page solves the equations themselves.

Waves, light and quanta

L2: school

Bending light

PHYA lens is a boundary that somebody curved, and no page on this path introduces physics the first one does not already contain. What changes is how much is asked of it: one surface, then an ideal lens, then a piece of glass.

L2: school

From one spring to a standing wave

PHYOne restoring force, followed as far as it will go. A mass on a spring oscillates, a row of them passes the oscillation along, two of those meeting decide whether to add or cancel, and a boundary at each end throws away every frequency that does not fit.

L2: school

Wave optics

PHYRay optics says light goes straight and an edge casts a sharp shadow. Each page here draws that answer as a ghost beside the wave answer, and what stands in the light's way changes from page to page: two surfaces, one slit, a round aperture, and finally an opaque disc whose shadow is bright at its centre.

L2: school

Quantum mechanics: matter as waves

PHYLight arrives in packets, and the same constant h then gives every particle a wavelength. The rest follows from taking that wave seriously: made to fit a box, it has a lowest energy that is not zero; it leaks through walls it cannot climb; and squeezed into a small space it spreads over many wavenumbers, which is the uncertainty principle.

L3: undergraduate

The heat, wave and Laplace equations

PHYThree equations built on one operator, the Laplacian, that differ only in what time does. Heat forgets, the sharpest detail first. A wave carries a disturbance away, and on a sheet never quite finishes arriving. Laplace's equation has no time in it at all, and it is where heat forgets its way to: every point the average of its neighbours.

Electricity and magnetism

L1: foundations

What Ohm’s law leaves out

PHYOhm’s law, as its own page says, describes one resistor at a steady temperature, on direct current, with nothing else in the loop. Each page after it puts back one of the things that sentence left out: a second component, the wire, the battery, a circuit that will not reduce, and a voltage that changes.

L2: school

Resistance, then reactance

PHYA capacitor has no resistance and limits the current anyway, and what it sets is a time rather than a number of ohms. The second page shows that the time belongs to any system with one store and one drain. The third adds a second store, and the time becomes a frequency.

L2: school

What is not a resistor

PHYOhm's law describes one kind of part. The five here store energy in a voltage or a current, conduct in one direction, amplify, and amplify precisely, and each is unreliable on its own: a transistor's current gain β varies threefold between samples of the same type. The circuit around a component is what makes it predictable, and every page shows how.

L3: undergraduate

Where fields come from

PHYCharges make electric fields and currents make magnetic ones, and the exam question is always which field comes from which arrangement. The chapter adds up pieces first, with an integral and the symmetry that cancels most of it, then takes the shortcuts symmetry allows: Gauss's law for charge, and the Biot–Savart law and Ampère's law for current, ending where Ampère's law needs Maxwell's correction.

Geometry and trigonometry

L2: school

Circles and waves are the same motion

MATHThree tools, and the point of the sequence is that they are not three subjects. A sine wave is what uniform circular motion looks like from the side, and a swinging pendulum is what it looks like when gravity supplies the turning.

Bio, Geo, Chem

L3: undergraduate

How a weather forecast is made

GEOA forecast is a model run forward from a starting state nobody knows exactly, so forecasters run it many times and let the disagreement say how far to trust it. The second page opens the model and finds a way to fail that has nothing to do with chaos. The third goes back to Lorenz's equations of 1963, where the run's position is soon lost and the shape it draws never is.

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