This is a free teaching resource for students preparing for GCSE and A-Level Physics exams (AQA, OCR and Edexcel specifications). Everything here is aimed at exam success: clear explanations of every topic on the syllabus, all the essential equations, links to each exam board's past papers, and practical guidance on revision technique. Create a free student account to track your revision and log your past-paper scores — see Accounts.
Physics is the study of matter, energy, forces, and the fundamental interactions that govern the universe. The notes are organised into ten themes, from motion and forces through to relativity, matching the order topics are usually taught. The Topics grid below links straight to any subtopic. For each one, the key equations are in bold — learn the equation first, then work through the examples.
How to use this site: The menu at the top jumps between Topics, Revision guidance, and Past Papers. Synoptic exam questions (worth around 15% of A-Level marks) ask you to combine ideas from different themes, so the notes cross-reference related topics throughout. If you spot an error or want an additional topic added, email the address in the Contact section below.
Last updated: June 2024. Covers AQA (7407/8464), OCR A (H556/J250) and Edexcel (9PH0/1PH0) specifications. Suitable for independent study or classroom use.
Every topic across the GCSE and A-Level specifications, grouped the way they are taught. Click any subtopic to jump to its notes.
Distance is the total path length travelled (a scalar); displacement is the straight-line distance from start to finish in a given direction (a vector). Speed is the rate of change of distance (scalar); velocity is the rate of change of displacement (vector): v = Δs/Δt. Acceleration is the rate of change of velocity: a = Δv/Δt (unit: m s−2). A negative acceleration (deceleration) means the object is slowing down, or speeding up in the negative direction.
Motion graphs. On a displacement–time graph, the gradient is the velocity; a curve means changing velocity (acceleration). On a velocity–time graph, the gradient is the acceleration and the area under the line is the displacement. A horizontal line means constant velocity; a straight slope means uniform acceleration. These graphical relationships are tested in nearly every mechanics paper, so practise reading gradients and areas quickly.
For motion with constant acceleration, the four "suvat" equations relate displacement s, initial velocity u, final velocity v, acceleration a and time t:
v = u + at · s = ut + ½at² · v² = u² + 2as · s = ½(u + v)tChoose the equation that contains the three quantities you know plus the one you want. Projectile motion is solved by resolving into independent horizontal and vertical components: horizontal velocity is constant (no force), while the vertical motion has constant downward acceleration g ≈ 9.81 m s−2. The two motions share the same time of flight. A body dropped and a body thrown horizontally from the same height hit the ground simultaneously. Terminal velocity is reached when drag equals weight, so the resultant force — and therefore acceleration — falls to zero (see Friction).
First law: a body stays at rest or moves at constant velocity unless acted on by a resultant force. This defines inertia — the resistance of mass to changes in motion. Second law: the resultant force is proportional to the rate of change of momentum, which for constant mass gives F = ma (F in newtons, m in kg, a in m s−2). Third law: if body A pushes on body B, then B pushes back on A with an equal and opposite force — the two forces act on different bodies and are of the same type. A body in equilibrium has zero resultant force and zero resultant moment about every point.
A force is a push or pull (a vector, unit: newton). Common forces: weight W = mg (always vertically down), the normal contact force (perpendicular to a surface), tension (along a rope), friction and drag (oppose motion), and upthrust (buoyancy). The resultant of several forces is their vector sum; forces at angles are added by resolving into perpendicular components (see Vectors & Scalars). A free-body diagram shows all forces on a single object and is the first step in almost every mechanics problem.
A moment (turning effect) is M = Fd, where d is the perpendicular distance from the pivot to the line of action of the force (unit: N m). For rotational equilibrium, the principle of moments states the sum of clockwise moments about a pivot equals the sum of anticlockwise moments. A couple is a pair of equal, opposite, parallel forces; its moment is force × perpendicular separation. The centre of mass is the single point at which the whole weight of a body can be taken to act.
Friction is the force opposing the relative sliding of two surfaces in contact. Static friction adjusts to prevent motion up to a maximum value; once the object slides, kinetic (dynamic) friction acts and is roughly constant. To a good approximation the maximum frictional force is proportional to the normal contact force: F ≤ μN, where μ is the coefficient of friction. Friction converts kinetic energy into heat.
Drag (air/fluid resistance) increases with speed, so a falling object accelerates until drag grows to equal its weight; at that point the resultant force is zero and it falls at constant terminal velocity. Friction and drag are why real machines are never 100% efficient (see Energy).
Linear momentum is p = mv (a vector, unit: kg m s−1). The principle of conservation of momentum states that in a closed system (no external resultant force) the total momentum before an interaction equals the total momentum after it. This holds for all collisions and explosions. In two dimensions, momentum is conserved independently in each perpendicular direction.
In an elastic collision, kinetic energy is also conserved (e.g. ideal gas molecules, snooker balls to a good approximation). In an inelastic collision, momentum is conserved but some kinetic energy is converted to heat, sound or deformation; in a perfectly inelastic collision the bodies stick together and move with a common velocity. Always set a positive direction first, then treat momentum in the opposite direction as negative.
Impulse is the change in momentum produced by a force acting over time: impulse = FΔt = Δp = mv − mu (unit: N s, equivalent to kg m s−1). On a force–time graph, the impulse is the area under the curve. Because Δp is fixed by a collision, increasing the contact time Δt reduces the peak force — the principle behind airbags, crumple zones, crash mats and catching a ball by drawing your hands back. Conversely, a short, hard impact (a hammer, a karate strike) delivers a large force in a brief time.
Work done by a force is W = Fs cosθ (force × distance moved in the direction of the force; unit: joule, J). Kinetic energy Ek = ½mv². Gravitational potential energy near Earth's surface Ep = mgh. Elastic potential energy in a stretched spring Ee = ½k(Δx)². The work–energy theorem states the net work done on a body equals its change in kinetic energy.
Power is the rate of doing work or transferring energy: P = W/t = E/t, and for a force moving at velocity v, P = Fv (unit: watt, W = J s−1). Efficiency = useful energy (or power) output ÷ total energy (or power) input, always less than 1 (or 100%) because some energy is dissipated, usually as heat.
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred between stores or converted between forms. The total energy of a closed system is constant. Energy is held in stores — kinetic, gravitational, elastic, thermal, chemical, nuclear, electrostatic, magnetic — and moved between them by pathways: mechanical work, electrical work, heating, and radiation. For a falling object (ignoring drag), lost gravitational PE equals gained kinetic energy: mgh = ½mv². In real systems, "wasted" energy is dissipated to the surroundings as heat and becomes too spread out to be useful, but it is never lost.
Internal energy is the sum of the randomly distributed kinetic and potential energies of all the particles in a body. Temperature (in kelvin) is a measure of the average kinetic energy per particle; absolute zero (0 K = −273 °C) is where particle motion is minimum. Specific heat capacity c is the energy to raise 1 kg of a substance by 1 K: Q = mcΔT. Specific latent heat L is the energy to change the state of 1 kg without a temperature change: Q = mL (fusion for melting, vaporisation for boiling).
For an ideal gas: pV = nRT (n = moles, R = 8.31 J mol−1 K−1) or equivalently pV = NkT (N = molecules, k = 1.38 × 10−23 J K−1). Kinetic theory links the two scales: the mean kinetic energy of a molecule is ½m<c²> = (3/2)kT. The first law of thermodynamics states ΔU = Q − W (change in internal energy = heat supplied − work done by the gas), an expression of energy conservation. The second law states that heat flows spontaneously only from hot to cold and that the entropy (disorder) of an isolated system never decreases.
Newton's law of gravitation: every point mass attracts every other with a force F = GMm/r², where G = 6.67 × 10−11 N m² kg−2. This is an inverse-square law — double the separation and the force falls to a quarter. The gravitational field strength is the force per unit mass: g = F/m = GM/r² (unit: N kg−1, equal to the acceleration of free fall). Near a surface g is roughly uniform; far away it weakens with distance. Gravitational potential V is the work done per unit mass to bring a mass from infinity: V = −GM/r (always negative; zero at infinity), and gravitational PE is Ep = −GMm/r.
For a satellite in a circular orbit, gravity provides the centripetal force, so GMm/r² = mv²/r, giving orbital speed v = √(GM/r) — lower, faster orbits; higher, slower ones. Combining with v = 2πr/T leads to Kepler's third law: T² ∝ r³ (the square of the orbital period is proportional to the cube of the orbital radius). Kepler's other laws: planets move in ellipses with the Sun at one focus (1st), and a line from planet to Sun sweeps equal areas in equal times (2nd).
A geostationary satellite orbits with a period of exactly 24 hours, directly above the equator, so it stays over one point on Earth — ideal for communications. Escape velocity is the minimum speed to escape a body's gravity entirely: vesc = √(2GM/r). The total energy of an orbiting body (kinetic + potential) is negative and constant; as it loses energy to drag it spirals inwards and speeds up.
Charge (symbol Q, unit: coulomb, C) is a fundamental property of matter; it is conserved and quantised in units of the elementary charge e = 1.60 × 10−19 C. Like charges repel, unlike charges attract. Conductors (metals) have free electrons that move easily; insulators do not, so they hold static charge. Objects can be charged by friction (transferring electrons) or by induction. Current is the rate of flow of charge: I = ΔQ/Δt (see Electricity).
Coulomb's law gives the force between two point charges: F = Qq/(4πε₀r²), where ε₀ = 8.85 × 10−12 F m−1 is the permittivity of free space — another inverse-square law, exactly analogous to gravitation but able to attract or repel. The electric field strength is the force per unit positive charge: E = F/q; for a radial field E = Q/(4πε₀r²), and for a uniform field between parallel plates E = V/d (unit: N C−1 or V m−1). Field lines point from positive to negative and show the direction of force on a positive charge.
Electric potential V at a point is the work done per unit positive charge to bring it from infinity: V = Q/(4πε₀r) (unit: volt, V = J C−1). Unlike gravitational potential it can be positive or negative. The potential energy of a charge q at potential V is E = qV; the work to move a charge between two points is W = qΔV. Equipotentials are surfaces of constant potential, always perpendicular to field lines; no work is done moving along one. A capacitor stores charge on two plates, Q = CV, holding energy E = ½QV = ½CV².
A magnetic field is the region where a magnetic material or moving charge feels a force; field lines run from north to south outside a magnet. An electric current creates a magnetic field (electromagnetism). A current-carrying wire in a field experiences the motor effect: F = BIL, where B is the magnetic flux density (unit: tesla, T). A charge moving through a field feels F = BQv (the magnetic part of the Lorentz force). Directions are given by Fleming's left-hand rule (thumb = force, first finger = field, second finger = current).
Electromagnetic induction: a changing magnetic flux through a coil induces an e.m.f. equal to the rate of change of flux linkage: ε = −N(dΦ/dt) (Faraday's law), where Φ is the flux (unit: weber, Wb) and N the number of turns. The minus sign is Lenz's law: the induced current opposes the change that causes it (conserving energy). A transformer uses this to change a.c. voltage: Vp/Vs = Np/Ns, with current inversely related (VpIp = VsIs for an ideal transformer). Step-up transformers raise voltage for efficient grid transmission; step-down transformers lower it for safe use.
Current I = ΔQ/Δt (unit: ampere, A) is the rate of flow of charge; conventional current flows from + to −, opposite to electron flow. Potential difference (voltage) is the energy transferred per unit charge: V = W/Q (unit: volt). Resistance R = V/I (unit: ohm, Ω). Ohm's law states that for an ohmic conductor at constant temperature, current is proportional to voltage, so R is constant. Resistivity ρ is a material property: R = ρL/A — a longer or thinner wire has more resistance.
Electrical power is the rate of energy transfer: P = IV = I²R = V²/R (unit: watt). Energy transferred is E = Pt = IVt (joules), or in domestic billing, kilowatt-hours: energy (kWh) = power (kW) × time (h), with cost = energy × price per unit. Because power lost as heat in a cable is I²R, the National Grid transmits at very high voltage and low current to minimise losses, using transformers to step up and back down (see Magnetism).
Kirchhoff's first law (current law): the total current into a junction equals the total current out — a statement of conservation of charge. Kirchhoff's second law (voltage law): around any complete loop, the sum of the e.m.f.s equals the sum of the potential differences — a statement of conservation of energy.
These give the rules for combining resistors. In series: the same current flows through each, voltages add, and Rtotal = R₁ + R₂ + …. In parallel: the voltage across each is the same, currents add, and 1/Rtotal = 1/R₁ + 1/R₂ + … (so the combined resistance is always less than the smallest branch).
The I–V characteristic of a component reveals its behaviour:
| Component | I–V behaviour |
|---|---|
| Fixed resistor / metal wire (ohmic) | Straight line through the origin — constant resistance. |
| Filament lamp | S-shaped curve — resistance rises as the filament heats up. |
| Diode / LED | Conducts only one way, above a threshold (~0.7 V); near-zero current in reverse. |
| Thermistor (NTC) | Resistance falls as temperature rises — used as a temperature sensor. |
| LDR | Resistance falls as light intensity rises — used as a light sensor. |
A real cell has internal resistance r, so its e.m.f. ε (energy per unit charge supplied) splits between the external circuit and itself: ε = I(R + r) = V + Ir, where V is the terminal p.d. A potential divider splits a supply voltage with two resistors: Vout = Vin × R₂/(R₁ + R₂); replacing one resistor with a thermistor or LDR makes an automatic sensing circuit.
A wave transfers energy without transferring matter. In a transverse wave the oscillations are perpendicular to the direction of travel (light, water, EM waves); in a longitudinal wave they are parallel (sound). The wave equation is v = fλ. Frequency f is oscillations per second (unit: hertz); period T = 1/f; wavelength λ is the distance between points in phase; amplitude is the maximum displacement. Phase difference is measured in degrees or radians; in-phase points differ by a whole number of wavelengths. A standing wave forms when two identical waves travel in opposite directions, producing fixed nodes and antinodes at resonant frequencies.
The principle of superposition: when waves meet, the resultant displacement is the vector sum of the individual displacements. Constructive interference (amplitudes add) occurs where the path difference is a whole number of wavelengths, nλ; destructive interference (amplitudes cancel) occurs at an odd number of half-wavelengths, (n + ½)λ. Stable patterns need coherent sources (constant phase difference, same frequency). In Young's double-slit experiment the fringe spacing is w = λD/s (D = slit-to-screen distance, s = slit separation). A diffraction grating with spacing d gives sharp maxima at d sinθ = nλ. Interference of light is direct evidence of its wave nature.
Light is part of the electromagnetic spectrum (in order of increasing frequency/energy: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma), all travelling at c = 3.00 × 108 m s−1 in a vacuum. Refraction is the change of speed (and bending) as light crosses between media; Snell's law is n₁ sinθ₁ = n₂ sinθ₂, where the refractive index n = c/v. Total internal reflection occurs beyond the critical angle sinθc = 1/n, the basis of optical fibres. Light also reflects (angle of incidence = angle of reflection) and disperses into colours because refractive index depends on wavelength.
Light also behaves as particles called photons, each with energy E = hf = hc/λ, where h = 6.63 × 10−34 J s (Planck's constant). The photoelectric effect — electrons emitted instantly from a metal only above a threshold frequency, regardless of intensity — cannot be explained by waves and is described by Einstein's equation hf = φ + Ek(max), where φ is the work function. Electrons in atoms occupy discrete energy levels; a photon is emitted or absorbed when an electron jumps between them, hf = E₁ − E₂, producing characteristic line spectra. Matter is also wave-like: the de Broglie wavelength is λ = h/p = h/mv, confirmed by electron diffraction. This wave–particle duality is the foundation of quantum physics.
Einstein's 1905 theory rests on two postulates: (1) the laws of physics are the same in all inertial (non-accelerating) frames, and (2) the speed of light in a vacuum, c, is the same for every observer regardless of their motion or the source's. The consequences are profound. Time dilation: a moving clock runs slow, t = t₀ γ; length contraction: a moving object is shortened along its motion, L = L₀/γ; where the Lorentz factor is γ = 1/√(1 − v²/c²). Simultaneity is relative — events simultaneous in one frame need not be in another.
Mass and energy are equivalent: E = mc², with total energy E = γmc² and a rest energy mc² even when stationary. No object with mass can reach c, because its energy would become infinite. Time dilation is verified daily — cosmic-ray muons reach the ground that should have decayed first, and GPS satellite clocks must be corrected for it.
Einstein's 1915 theory extends relativity to gravity and acceleration. Its equivalence principle states that being in a gravitational field is locally indistinguishable from accelerating — you cannot tell, inside a sealed lift, whether your weight is due to gravity or to the lift accelerating upward. The central idea: mass and energy curve spacetime, and what we perceive as gravity is matter following the straightest possible path (a geodesic) through that curved geometry. "Spacetime tells matter how to move; matter tells spacetime how to curve."
Predictions confirmed by experiment include the bending of starlight by the Sun (Eddington, 1919), gravitational time dilation (clocks run slower in stronger gravity), the precession of Mercury's orbit, gravitational lensing of distant galaxies, black holes (regions where escape velocity exceeds c), and gravitational waves — ripples in spacetime first detected directly by LIGO in 2015.
Physics uses the SI system, built on seven base units; five appear at this level: the metre (m), kilogram (kg), second (s), ampere (A) and kelvin (K). All other units are derived from these — for example the newton is kg m s−2, the joule is kg m² s−2, and the watt is J s−1. Prefixes scale units in powers of ten:
| Prefix | Symbol | Factor | Prefix | Symbol | Factor | |
|---|---|---|---|---|---|---|
| tera | T | 1012 | milli | m | 10−3 | |
| giga | G | 109 | micro | µ | 10−6 | |
| mega | M | 106 | nano | n | 10−9 | |
| kilo | k | 103 | pico | p | 10−12 |
A valid equation must be homogeneous — the units on both sides must match; checking this (dimensional analysis) catches many algebra slips. Report measurements to a sensible number of significant figures and quote the uncertainty: absolute (± a value), fractional, or percentage. Uncertainties add for sums and differences, and combine as percentages for products, quotients and powers.
A scalar has magnitude only (mass, time, energy, speed, temperature, distance). A vector has both magnitude and direction (displacement, velocity, acceleration, force, momentum, field strength). Vectors are drawn as arrows whose length shows magnitude.
To add vectors, place them head-to-tail; the resultant runs from the start of the first to the end of the last (the triangle or parallelogram rule). For two perpendicular vectors the resultant has magnitude R = √(x² + y²) at angle θ = tan−1(y/x). The reverse — resolving a vector into perpendicular components — is used constantly: a force F at angle θ to the horizontal has components Fx = F cosθ and Fy = F sinθ. Resolving is the key to inclined-plane, projectile and equilibrium problems throughout the course.
Effective revision requires active retrieval and repeated practice. Below is a recommended routine for each topic:
Key equations are provided in the sections above. Revision summary sheets and mark schemes are available on request.
Past papers are the single most valuable revision resource: they show you the exact style and difficulty of questions you'll face, and they reveal which topics are frequently tested. The official mark schemes and examiners' reports are free — direct links below.
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