Find your way through physics, mathematics, chemistry and materials science.

An atom has a tiny, dense, positively charged nucleus made of protons and neutrons, surrounded by electrons; atoms of the same element with different neutron counts are called isotopes.

Capacitance measures how much charge a component can store per volt across it, and a charged capacitor holds energy in the electric field between its plates.

When quantities are added or subtracted their absolute uncertainties add; when they are multiplied or divided their relative uncertainties add.

Energy cannot be created or destroyed, only converted between forms — the total energy of an isolated system stays constant.

In a system with no external forces, the total momentum before an interaction equals the total momentum after it.

Displacement, velocity and acceleration are vectors: each has a direction as well as a size, unlike the distance and speed used at a lower level.

Electric charge comes in two kinds, positive and negative, and an electric current is simply charge flowing through a conductor over time.

An electric charge creates an electric field around it, and any other charge placed in that field feels a force proportional to the field strength there.

A changing magnetic field through a loop of wire induces an electromotive force in it — the faster the field changes, the larger the induced voltage.

A changing electric field creates a changing magnetic field and vice versa, and this self-sustaining pair propagates through space as an electromagnetic wave, including visible light.

The second law of thermodynamics says the entropy of an isolated system never decreases, which is why heat flows from hot to cold and not the other way round.

For an ideal gas, pressure, volume, temperature and the amount of substance are linked by a single equation: pV equals nRT.

When two waves overlap they add together point by point — interference — and a wave passing through a narrow opening spreads out into the region behind it — diffraction.

A gas's temperature is a measure of the average kinetic energy of its particles, which move randomly and collide elastically with each other and the container walls.

The first law of thermodynamics says energy is conserved: the change in a system's internal energy equals the heat added minus the work done by it.

A converging lens bends parallel rays of light so that they meet at its focal point, and the focal length measures how far away that point is.

Moving charges and electric currents create magnetic fields, and a magnetic field in turn exerts a force on any moving charge that crosses it.

Precision describes how repeatable a measurement is; accuracy describes how close it is to the true value — a measurement can have one without the other.

Impulse is the product of a force and the time it acts for, and it equals the change in an object's momentum.

Every pair of masses attracts each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

An object stays at rest or keeps moving at constant velocity unless a net force acts on it — this resistance to a change in motion is inertia.

Force equals mass times acceleration.

Whenever one object exerts a force on a second object, the second exerts an equal and opposite force back on the first.

During a phase transition such as melting or boiling, the energy added goes into breaking bonds between particles rather than raising the temperature, which stays constant until the transition is complete.

Light striking a metal surface ejects electrons only if a single photon carries enough energy to free one, no matter how bright the light is — evidence that light behaves as particles, not just waves.

Light delivers its energy in discrete packets called photons, each carrying an energy proportional to the light's frequency.

A physical quantity is a number together with a unit; SI fixes seven base units that every other unit is built from.

Light is a transverse wave whose electric field can oscillate in any direction perpendicular to its motion; polarizing it restricts that oscillation to a single direction.

For a general function of measured quantities, the uncertainty in the result is found from the function's partial derivatives with respect to each input.

An electron bound in an atom can only occupy certain discrete energy levels, and it absorbs or emits a photon of exactly the right energy when it jumps between them.

An unstable nucleus can spontaneously decay, emitting radiation; its half-life is the time it takes for half of a sample of that isotope to decay.

Light reflects off a surface at the same angle it arrives, and refracts — changes direction — when it passes from one transparent material into another.

When a system is driven at its natural oscillation frequency, the amplitude of its response grows much larger than it would at any other driving frequency.

A scalar has only magnitude; a vector has both magnitude and direction, and the two must never be added together.

Significant figures record how precisely a measured or calculated value is known, and a result can never be more precise than its least precise input.

In simple harmonic motion the restoring force is proportional to the displacement from equilibrium and always points back towards it, producing a smooth, repeating oscillation.

Snell's law relates the angles of incidence and refraction to the refractive indices of the two materials: a ray bends more the greater the difference between them.

Specific heat capacity is the energy needed to raise the temperature of one kilogram of a substance by one degree, and it differs widely between materials.

Speed is the distance an object covers divided by the time it takes, and it tells you nothing about the direction the object is moving.

A standing wave forms when two identical waves travel in opposite directions and interfere, producing fixed points of no displacement, called nodes, that never move.

Temperature measures how hot or cold something is; heat is energy that flows between objects because they are at different temperatures.

Most materials expand when heated because their particles move faster and take up more space on average.

Beyond a critical angle, light travelling into a less dense material reflects entirely back rather than refracting through, which is how optical fibres trap light inside them.

Uncertainty is the range within which the true value is expected to lie; error is the difference between a measured value and the true value, which is usually unknown.

Voltage drives current through a circuit, and resistance opposes it — for many materials the three are linked by Ohm's law: voltage equals current times resistance.

Passing light through two closely spaced slits produces an interference pattern of bright and dark fringes, direct evidence that light behaves as a wave.

Every particle, including electrons, has an associated wavelength, and every wave, including light, can transfer energy and momentum in discrete particle-like packets.

A wave's speed equals its frequency times its wavelength, so for a wave travelling at a fixed speed, a higher frequency always means a shorter wavelength.

A wave carries energy from place to place through repeating oscillations, without the medium itself travelling along with it.

Work is done when a force moves an object through a distance, and it transfers energy from one form or object to another.