This is a free teaching resource for students preparing for GCSE and A-Level Physics exams (AQA and OCR specifications). Everything here is aimed at exam success: clear explanations of key concepts, all the essential equations, and practical guidance on revision technique.
Physics is the study of matter, energy, forces, and the fundamental interactions that govern the universe. At GCSE, you'll master classical mechanics, electricity, waves, and basic nuclear physics. At A-Level, you'll go deeper into these topics, plus thermal physics, fields, and quantum mechanics. The synoptic questions on A-Level papers (worth 15% of marks) require you to combine knowledge from different modules — these notes are organized to help you see the connections.
How to use this site: The menu above jumps to A-Level modules, GCSE topics, revision guidance, and past papers. For each topic, the key equations are in bold. Learn the equation first, then work through examples. When revising, use the past papers section to practise under exam conditions. If you find an error or want to suggest an additional topic, email the address in the Contact section below.
Last updated: June 2024. Covers AQA (7407/8464) and OCR A (H555) specifications. All material is suitable for independent study or classroom use.
A-Level Physics covers eight major themes: (1) Measurements, uncertainties and data analysis — how to report results with errors and uncertainty. (2) Mechanics — forces, motion, energy, and momentum, from Newton to relativity. (3) Materials — how solids deform under stress. (4) Waves and optics — interference, diffraction, refraction, and the wave-particle duality. (5) Electricity — circuits, current, resistance, and electromagnetic induction. (6) Further mechanics and thermal physics — circular motion, SHM, gas laws, and thermodynamics. (7) Fields — gravity, electric fields, magnetic fields, and the inverse-square law. (8) Nuclear physics — radioactivity, binding energy, and fission/fusion. The equations listed below are the ones the exam boards expect you to know and apply without being given them.
Newton's laws: (1) A body remains at rest or moves at constant velocity unless acted upon by a resultant force. (2) F = ma, where F is the resultant force in newtons, m is mass in kg, and a is acceleration in m s−2. (3) Forces come in equal and opposite pairs acting on different bodies. A body in equilibrium has zero resultant force and zero resultant moment about any point.
The equations of motion (constant acceleration, the "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. For a projectile, resolve into horizontal (constant velocity) and vertical (constant acceleration g ≈ 9.81 m s−2 downward) components.
Work, energy and power: Work done W = Fs cosθ (force × displacement × cosine of angle). Kinetic energy Ek = ½mv². Gravitational PE Ep = mgh (near Earth's surface). The work-energy theorem states W = ΔEk. Power is P = W/t = Fv (in watts). Energy is conserved: total mechanical energy is constant in the absence of non-conservative forces.
A moment (or torque) 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 sum of clockwise moments about a pivot equals the sum of anticlockwise moments (principle of moments). Momentum p = mv (unit: kg m s−1). Momentum is conserved in all collisions. Impulse is FΔt = Δp. Kinetic energy is conserved only in elastic collisions; in inelastic collisions, some KE is converted to other forms (heat, sound, deformation).
Hooke's law: F = kΔL, where k is the spring constant (N m−1) and ΔL is the extension. This is linear only within the limit of proportionality; beyond that, the material becomes permanently deformed. Elastic deformation is reversible; plastic deformation is permanent.
Stress σ = F/A (force per unit cross-sectional area, unit: Pa). Strain ε = ΔL/L (fractional change in length, dimensionless). The Young modulus E = σ/ε (unit: Pa) measures the stiffness of a material — how much stress is needed to produce a given strain. For a wire, E = F/A × L/ΔL. The area under a force–extension graph is the elastic strain energy stored: E = ½k(ΔL)². The breaking strength of a material is reached when strain becomes too large; the stress at which this occurs is the ultimate tensile strength.
Current I = ΔQ/Δt (unit: ampere, A) is the rate of flow of charge. Ohm's law states V = IR for an ohmic conductor (one with constant resistance) at constant temperature. Electrical power is P = IV = I²R = V²/R (unit: watt, W). Electrical energy dissipated is E = Pt = IVt.
Resistors in series add: Rtotal = R₁ + R₂ + …; in series, the current is the same through each, but voltages add. Resistors in parallel obey 1/Rtotal = 1/R₁ + 1/R₂ + …; in parallel, the voltage is the same across each, but currents add. Resistivity ρ is a material property; R = ρL/A, where L is length and A is cross-sectional area. A longer or thinner wire has higher resistance.
The electromotive force (e.m.f.) ε of a source is the energy supplied per unit charge. The terminal pd (potential difference) V is the actual voltage available at the terminals: ε = I(R + r), where r is the internal resistance. When no current flows (open circuit), V = ε. A potential divider uses resistors to split a supply voltage: Vout = Vin × R₂/(R₁ + R₂). This is the principle behind a rheostat or potentiometer.
The wave equation is v = fλ: wave speed equals frequency times wavelength. Frequency f is the number of oscillations per second (unit: hertz, Hz). Period T is the time for one complete oscillation, so f = 1/T. Amplitude is the maximum displacement from equilibrium. Wavelength λ is the distance between successive crests (or any two points in phase).
Superposition is the principle that when two or more waves meet, the resultant displacement is the vector sum of individual displacements. Constructive interference occurs when the path difference is a whole number of wavelengths (nλ, where n is an integer); amplitudes add, giving a bright fringe. Destructive interference occurs at path difference of an odd number of half-wavelengths ((2n+1)λ/2); amplitudes cancel, giving a dark fringe. Coherence requires constant phase difference (e.g., from two coherent sources or a single source split by a double slit).
For double-slit interference, the fringe spacing is w = λD/s, where D is the distance to the screen and s is the slit separation. A diffraction grating has many equally spaced slits; bright fringes obey d sinθ = nλ (where d is the slit spacing, n is the order). Refraction is the bending of light when passing between media. Snell's law states n₁ sinθ₁ = n₂ sinθ₂, where θ is measured from the normal. The refractive index n = c/v (speed of light in vacuum divided by speed in the medium). Total internal reflection occurs when light tries to exit a denser medium at an angle beyond the critical angle: sinθc = 1/n (relative refractive index). For angles greater than θc, all light is reflected; none is refracted.
Gravitational field strength g is the gravitational force per unit mass at a point (unit: N kg−1 or m s−2). g = GM/r², where G is the gravitational constant (6.67 × 10−11 N m² kg−2), M is the source mass, and r is distance. Newton's law of gravitation gives the force between two point masses: F = GMm/r². This is an inverse-square law: force is proportional to 1/r². Gravitational potential energy Ep = −GMm/r (negative because zero potential is at infinite distance).
For electric fields, Coulomb's law gives the force between two point charges: F = Qq/(4πε₀r²), where ε₀ is the permittivity of free space (8.85 × 10−12 F m−1). The electric field strength E is the force per unit charge: E = Q/(4πε₀r²) (unit: N C−1 or V m−1). Both gravitational and electric fields are radial and follow inverse-square laws.
A charge moving perpendicular to a magnetic field experiences a force F = BQv (the Lorentz force). A current-carrying wire in a magnetic field feels F = BIL, where B is magnetic flux density (unit: tesla, T), I is current, and L is length. The direction is given by the Fleming left-hand rule. Electromagnetic induction: The induced e.m.f. is the rate of change of magnetic flux linkage, ε = −N(dΦ/dt) (Faraday's law), where N is the number of turns and Φ is magnetic flux (unit: weber, Wb). The negative sign reflects Lenz's law: the induced e.m.f. opposes the change causing it. A transformer uses two coils; for an ideal transformer, Vp/Vs = Np/Ns = Is/Ip (where p = primary, s = secondary). Step-up transformers increase voltage; step-down reduce it.
For circular motion, the velocity is always perpendicular to the radius; the object moves in a circle at constant speed. The angular velocity ω is the angle rotated per unit time (unit: rad s−1); v = ωr. The centripetal acceleration is always directed toward the center: a = v²/r = ω²r. The centripetal force is F = mv²/r = mω²r; it is provided by gravity, tension, friction, or normal force, depending on the setup.
Simple harmonic motion (SHM) is oscillatory motion where acceleration is proportional to and opposite in direction to displacement: a = −ω²x. The displacement varies as x = A cos(ωt) (where A is amplitude). The period is T = 2π/ω. For a mass-spring system, T = 2π√(m/k); for a simple pendulum, T = 2π√(l/g) (where l is length). Energy in SHM oscillates between kinetic and potential; total energy E = ½k A².
The ideal gas law relates pressure p, volume V, temperature T, and amount of substance: pV = nRT, where n is the number of moles and R is the gas constant (8.31 J mol−1 K−1). Alternatively, pV = NkT, where N is the number of molecules and k is Boltzmann's constant (1.38 × 10−23 J K−1). The mean kinetic energy of a molecule is ½m<c²> = (3/2)kT. This links temperature (a macroscopic quantity) to molecular motion (microscopic). The first law of thermodynamics is ΔU = Q − W, where ΔU is change in internal energy, Q is heat added, and W is work done by the gas.
A photon is a quantum of electromagnetic radiation. Its energy is E = hf = hc/λ, where h is Planck's constant (6.63 × 10−34 J s), f is frequency, c is the speed of light (3 × 108 m s−1), and λ is wavelength. Photons have momentum p = E/c = h/λ.
The photoelectric effect is the emission of electrons from a metal surface when light shines on it. Einstein's photoelectric equation is hf = φ + Ek(max), where φ is the work function (the energy needed to remove an electron) and Ek(max) is the maximum kinetic energy of emitted electrons. Below the threshold frequency f₀ = φ/h, no electrons are emitted, no matter how bright the light. This particle nature of light contradicts the classical wave picture and supports quantum theory.
The de Broglie wavelength assigns a wavelength to any moving particle: λ = h/p = h/mv. This wavelength is very small for macroscopic objects but significant for electrons, which explains why electrons diffract in crystal lattices or around atomic nuclei — matter exhibits wave-like behavior.
Particle physics: Matter is built from quarks and leptons. Quarks combine to form hadrons (baryons like protons and neutrons; mesons). Leptons include electrons, muons, tau, and neutrinos. Every particle has a corresponding antiparticle with opposite charge; annihilation of a particle-antiparticle pair releases energy as photons (E = mc²).
The nucleus consists of protons and neutrons (nucleons). The mass number A is the total number of nucleons; the atomic number Z is the number of protons (which determines the element). Nucleon mass is about 1.67 × 10−27 kg; protons and neutrons have nearly equal mass, but the mass of a nucleus is slightly less than the sum of its constituent nucleons — this is the mass defect. The binding energy is Eb = Δmc², the energy released when nucleons combine. The binding energy per nucleon peaks around iron-56; this is why both fission (splitting heavy nuclei) and fusion (combining light nuclei) release energy and move toward the iron peak.
Radioactive decay is spontaneous and random; each nucleus decays independently with probability depending only on the decay constant λ. The activity (decay rate) is A = λN (unit: becquerel, Bq). The number of nuclei remaining after time t is N = N₀e−λt. The half-life t½ is the time for half the nuclei to decay: t½ = (ln 2)/λ ≈ 0.693/λ.
Alpha decay (AX → A−4Y + 4He): emits a helium nucleus (α particle), reducing A by 4 and Z by 2. These are energetic and easily stopped. Beta decay (AX → AY + 0e + νē): an electron (β particle) and antineutrino are emitted, increasing Z by 1. Beta particles penetrate further than alpha but are stopped by a sheet of aluminium. Gamma decay (AX* → AX + γ): emits a high-energy photon with no change in A or Z. Gamma rays are very penetrating and require lead or concrete shielding.
GCSE Physics covers five major themes: (1) Energy — stores, transfers, conservation, and efficiency. (2) Electricity — circuits, current, voltage, resistance, and the National Grid. (3) Forces and motion — Newton's laws, momentum, and collisions. (4) Waves — properties of waves, the electromagnetic spectrum, and uses of radiation. (5) Particle physics and radioactivity — the structure of atoms, radioactive decay, and half-life. Combined Science (Double Science) covers the same topics but in less depth; Separate Physics includes additional material such as circular motion and magnetic forces. The notes below apply to both; where a topic is Separate Physics only, it is marked.
Energy conservation: Energy cannot be created or destroyed; it is only converted from one form to another or transferred between objects. Useful devices convert energy into the form we want; real devices always waste some energy as heat due to friction, air resistance, etc. Kinetic energy is energy due to motion: Ek = ½mv². Gravitational potential energy (near Earth) is Ep = mgh, where h is height. Elastic potential energy stored in a stretched or compressed spring is Ee = ½ke² (or ½k(Δx)²). Other energy forms include thermal (heat), chemical (in fuel or batteries), nuclear, light, and sound.
Power is the rate of energy transfer: P = E/t (unit: watt, W = joule per second). P = IV for electrical power. Efficiency is a ratio measuring how well a device converts energy: efficiency = useful energy output / total energy input (dimensionless, or as a percentage). Real devices always have efficiency < 1 because some energy is wasted as heat.
Charge Q = It (unit: coulomb, C). Current is charge per second, I = Q/t (unit: amp, A). Potential difference (voltage) V = W/Q is the work done per unit charge. Electrical energy transferred is E = QV = IVt. For ohmic components, V = IR (Ohm's law). Electrical power P = IV = I²R (unit: watt, W).
Mains electricity in the UK is 230 V alternating current (a.c.) at 50 Hz (meaning it oscillates 50 times per second). The National Grid transmits electrical power across the country using transformers. A step-up transformer increases voltage (and decreases current) for transmission. This reduces heating losses (since P = I²R, loss is proportional to current squared). A step-down transformer then reduces the voltage back to safe levels (230 V) for homes. The transformer equation is Vp/Vs = Np/Ns (where p = primary, s = secondary coil).
Newton's three laws: (1) A body remains at rest or moves at constant velocity unless acted on by a resultant (net) force. (2) The resultant force on a body is proportional to its acceleration: F = ma. (3) If body A exerts a force on body B, then body B exerts an equal and opposite force on body A. Forces come in action-reaction pairs.
Weight is the gravitational force on an object: W = mg (unit: newton, N), where g ≈ 9.8 N kg−1 (or m s−2). Weight always acts downward. Mass is the amount of matter in an object (unit: kg); it is constant everywhere. Acceleration a = Δv/Δt (unit: m s−2) is the rate of change of velocity. If velocity increases, acceleration is positive (in the direction of motion); if it decreases, acceleration is negative (opposite to motion, or "deceleration"). Momentum p = mv (unit: kg m s−1) is conserved in collisions (the total momentum before equals the total after). This is true for both elastic and inelastic collisions.
Wave properties: All waves obey the wave equation v = fλ. Frequency f (Hz) is the number of oscillations per second; wavelength λ (m) is the distance between successive crests. Period T = 1/f. The electromagnetic spectrum, from longest to shortest wavelength, is: radio, microwave, infrared, visible light, ultraviolet, X-rays, gamma rays. Higher frequency means higher energy.
Particle model: Matter consists of tiny particles held together by forces. In solids, particles are tightly packed and vibrate in fixed positions (rigid shape, fixed volume). In liquids, particles are close but can move past each other (takes the shape of its container, fixed volume). In gases, particles are far apart and move freely (takes the shape and volume of its container). Density ρ = m/V (unit: kg/m³) is mass per unit volume.
Radioactivity: Some nuclei are unstable and decay by emitting radiation (alpha, beta, or gamma). This is random and spontaneous. Half-life is the time for half the nuclei in a sample to decay. After one half-life, half remain; after two half-lives, a quarter remain, etc. Half-life is constant for a given isotope.
Magnetism & electromagnetism: Magnets have two poles (north and south) and exert non-contact forces on each other and on iron. A magnetic field is the region around a magnet where magnetic forces act. An electric current through a wire creates a magnetic field (electromagnetism). This is the basis of the motor effect: a current-carrying wire in a magnetic field experiences a force, causing it to move. This principle is used in electric motors.
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 in the exam, and they reveal which topics are frequently tested.
All past papers and mark schemes are available from the exam board websites (aqa.org.uk, ocr.org.uk, thestudentroom.co.uk) or via the Lintoria archive. Attempt them under real exam conditions: no notes, calculator allowed, timed. Then mark ruthlessly against the scheme.
For questions about the notes or to report a mistake, email notes@lintoria.example. I aim to reply within a few days during term time.
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