A-Level Physics Study Guides

An object moving in a circular path at constant speed is continuously changing direction, which requires a resultant centripetal force directed toward the centre of the circle. In A-Level Physics, combining circular motion equations with Newton's Law of Gravitation explains satellite orbits, angular speed, and planetary motion.

Quantum physics examines how electromagnetic radiation and matter behave at the atomic scale through wave-particle duality. Key topics include photon energy (E = hf), Einstein's photoelectric effect equation, threshold frequency, atomic energy levels, and the de Broglie wavelength of moving particles.

An electric field is a region of space in which an electrically charged particle experiences an electrostatic force. This guide covers Coulomb's inverse-square law for point charges, uniform electric fields between parallel plates, electric potential, and how capacitors store charge and energy.

The Standard Model classifies subatomic matter into two fundamental families: hadrons (composite particles built from quarks that experience the strong nuclear force) and leptons (fundamental point particles such as electrons, muons, and neutrinos that do not feel the strong force). Hadrons subdivide into three-quark baryons (qqq, baryon number B = +1, all decaying eventually into the only stable baryon, the proton) and quark-antiquark mesons (qq̄, B = 0, such as pions and kaons). Every particle interaction is governed by four fundamental forces mediated by virtual exchange bosons (gluons/pions, photons, W⁺/W⁻/Z⁰ bosons, and gravitons) and must strictly conserve charge (Q), baryon number (B), and generation lepton numbers (Lₑ, L_μ), while strangeness (S) is conserved in strong interactions but can change by ΔS = 0 or ±1 in weak decays.

Wave interference and diffraction provide definitive proof of the wave nature of both mechanical oscillations and electromagnetic radiation. By the Principle of Superposition, when two coherent waves overlap in space, their instantaneous displacements add vectorially: producing stationary waves with fixed nodes and antinodes when two identical waves travel in opposite directions, or producing two-source interference fringes when coherent wavefronts spread out from slits. Learning the fundamental string resonance equation f₁ = (1 / 2L)√(T / μ), Young's double-slit fringe spacing w = λD / s, the diffraction grating equation d sin θ = nλ, and total internal reflection (sin θ_c = n₂ / n₁) in step-index optical fibres is essential for Paper 1 Physics.

Classical mechanics rests on vector resolution, static equilibrium, kinematics under uniform acceleration (SUVAT), and Newton's three laws of motion. Whether analysing a block sliding down an inclined plane at angle θ (where weight resolves into mg sin θ parallel to the slope and mg cos θ perpendicular to the slope) or a 2D projectile in flight (where horizontal velocity u cos θ remains constant while vertical velocity u sin θ accelerates downward at g = 9.81 m s⁻²), separating orthogonal components is the golden rule. Also, Newton's second law expressed as F = Δ(mv) / Δt links the area under a force-time graph directly to impulse, while the conservation of linear momentum governs every collision and explosion. Examiners regularly test multi-support bridge moments, projectile range/time-of-flight derivations, and proving whether a collision is elastic or inelastic.

Solid mechanics distinguishes between the extrinsic stiffness of a particular spring or wire (the spring constant k in Hooke's Law, F = kΔL) and the intrinsic stiffness of a material independent of its dimensions: the Young Modulus, E = Tensile Stress / Tensile Strain = (FL) / (AΔL). While the area under a Force-Extension (F-ΔL) graph gives the total elastic strain energy stored (E_p = ½FΔL = ½k(ΔL)²), the area under a Stress-Strain (σ-ε) graph gives the elastic strain energy stored per unit volume (½σε). In the laboratory, Young Modulus is determined using a long, thin metal wire to maximise extension ΔL while measuring diameter d at multiple positions with a micrometer screw gauge. Examiners frequently test springs in series and parallel, plastic deformation unloading lines, and comparing brittle (glass), ductile (copper), and polymeric (rubber) stress-strain graphs.

Direct current (DC) circuit analysis relies on two fundamental conservation laws formulated by Kirchhoff: conservation of electric charge at any junction (ΣI_in = ΣI_out) and conservation of energy around any closed loop (Σε = ΣIR). While metallic ohmic conductors maintain a constant resistance at constant temperature, heating a metal filament lamp increases lattice ion vibrations (raising resistance), whereas heating an NTC semiconductor thermistor or illuminating an LDR liberates mobile charge carriers into the conduction band (exponentially lowering resistance). Real power supplies possess internal resistance r, causing the terminal potential difference V to fall linearly with current I according to V = -rI + ε. Examiners heavily test sensor potential divider circuits, resistivity (R = ρL / A), and graphical determination of EMF ε and internal resistance r.

Simple Harmonic Motion (SHM) is the universal mathematical model for oscillatory systems, from a mass on a helical spring and a simple pendulum to vibrating quartz crystals and diatomic covalent bonds. An oscillation is strictly defined as SHM if and only if the acceleration a is directly proportional to the displacement x from the equilibrium position and is always directed toward the equilibrium position: a = -ω²x, where ω = 2πf = 2π/T is the angular frequency. Because velocity is the time derivative of displacement and acceleration is the time derivative of velocity, the x-t, v-t, and a-t sinusoidal graphs are shifted successively by π/2 radians (90°) in phase, while kinetic and potential energy exchange continuously so total mechanical energy E_total = ½mω²A² remains constant. Examiners test defining SHM from graphs, fiducial marker timing techniques, light/critical/heavy damping, and forced resonance curves.

Thermal physics links macroscopic properties of matter, temperature T, pressure p, volume V, and internal energy U - directly to the microscopic random kinetic and potential energies of atoms and molecules. While heating a solid or liquid without a state change raises average molecular kinetic energy (Q = mcΔT), heating at the melting or boiling point breaks intermolecular bonds to increase molecular potential energy at constant temperature (Q = ml). For an ideal gas (where intermolecular potential energy is zero), combining Boyle's, Charles's, and the Pressure Laws yields pV = nRT = NkT, which kinetic theory derives from Newton's laws of momentum change during elastic wall collisions as pV = ⅓Nm(c_rms)². In particular, equating these two expressions proves that the mean translational kinetic energy of a gas molecule depends solely on absolute Kelvin temperature: ½m(c_rms)² = (3/2)kT.

Newton's Law of Universal Gravitation states that every point mass attracts every other point mass with a force directly proportional to the product of their masses and inversely proportional to the square of their separation: F = GMm / r². Surrounding any mass M is a radial gravitational field of strength g = F / m = GM / r² (a vector pointing inward toward M) and a scalar gravitational potential V = -GM / r, which is always negative because gravitational potential is defined as zero at infinity and gravity is strictly attractive. Equating gravitational attraction to centripetal force (GMm / r² = mv² / r = mω²r) yields orbital speed v = √(GM / r), Kepler's Third Law T² = (4π² / GM)r³, total satellite energy E_total = -GMm / (2r), and escape velocity v_esc = √(2GM / R). Examiners regularly test potential gradient g = -ΔV / Δr, geostationary vs low-polar orbits, and why gravitational potential is negative.

A capacitor consists of two conducting plates separated by an insulating dielectric material, storing equal and opposite charges (+Q and -Q) when connected across a potential difference V according to Capacitance C = Q / V (in Farads, F = C V⁻¹). Inserting a polar dielectric of relative permittivity ε_r between the plates aligns molecular dipoles to create an opposing internal electric field, increasing capacitance by C = Aε₀ε_r / d. Because p.d. V increases linearly from 0 to V₀ as charge Q accumulates on the plates, the electrical energy stored is given by the triangular area under the V-Q graph: E = ½QV = ½CV² = ½Q²/C - meaning 50% of the energy supplied by a constant-voltage battery (QV) is inevitably dissipated as heat in the circuit resistance. Examiners heavily test the RC time constant τ = RC (37% / 63% rules), discharging vs charging exponential graphs, and linear ln(V) vs t plots.

A magnetic field of flux density B (measured in Tesla, T = N A⁻¹ m⁻¹ = Wb m⁻²) exerts a magnetic force on any moving electric charge or current-carrying conductor that has a component perpendicular to the magnetic field lines. Using Fleming's Left-Hand Rule (where the Second finger always points in the direction of conventional current, the motion of positive charge, or opposite to electron velocity), the magnetic force on a wire of length L is F = BIL sin θ, while the force on a single moving charge q is F = Bqv sin θ. Because the magnetic force F = Bqv is always strictly perpendicular (at 90°) to the particle's instantaneous velocity v, a uniform magnetic field does zero work on a charged particle (speed v and kinetic energy stay constant) and acts purely as a centripetal force (Bqv = mv² / r), bending the particle into a circle of radius r = mv / (Bq) with a constant frequency f = Bq / (2πm) exploited in particle cyclotrons.

Electromagnetic induction is the generation of an electromotive force (EMF, ε) whenever a conductor cuts magnetic field lines or whenever the magnetic flux linkage (NΦ = BAN cos θ, in Webers, Wb) through a coil changes over time. While Faraday's Law gives the magnitude of the induced EMF as directly proportional to the rate of change of magnetic flux linkage (ε = N ΔΦ / Δt), Lenz's Law gives its direction: the induced EMF and any resulting current always act in a direction that opposes the change in flux that produced it, which is a direct consequence of the Principle of Conservation of Energy. Rotating a rectangular coil at angular speed ω inside a uniform magnetic field generates an alternating EMF ε = BANω sin(ωt), whose root-mean-square values (V_rms = V₀ / √2 and I_rms = I₀ / √2) allow step-up and step-down transformers to transmit electrical power across the National Grid with minimal I²R heating losses.

Nuclear physics explores the structure, stability, and energy of atomic nuclei, beginning with Rutherford's alpha-scattering experiment which proved that an atom is mostly empty space with a tiny, dense, positively charged nucleus at its centre. High-energy electron diffraction reveals that nuclear radius obeys R = R₀ A^(1/3) (where R₀ ≈ 1.05-1.20 fm), proving that all nuclei have a constant, immense nuclear density (~10¹⁷ kg m⁻³). Unstable nuclei decay randomly and spontaneously toward the N-Z stability belt according to Activity A = -ΔN / Δt = λN and N = N₀ e^(-λt). Finally, Einstein's mass-energy equivalence (ΔE = Δmc², where 1 u = 931.5 MeV) explains why the Binding Energy per Nucleon curve peaks at Iron-56 (~8.8 MeV), allowing energy to be released both by nuclear fusion of light nuclei and by induced nuclear fission of heavy Uranium-235.

Astrophysics applies optics, quantum black-body radiation, and relativistic Doppler shifts to decode the universe. Astronomical telescopes use either converging lenses in normal adjustment (M = f_o / f_e, L = f_o + f_e) or parabolic Cassegrain mirrors to maximise collecting power (∝ D²) and angular resolution via the Rayleigh Criterion (θ ≈ λ / D). Stellar radiation is modelled as a black body governed by Wien's Displacement Law (λ_max T = 2.90 × 10⁻³ m K) and the Stefan-Boltzmann Law (P = σAT⁴), allowing astronomers to plot stars on the Hertzsprung-Russell (H-R) diagram and determine distances using the distance modulus formula m - M = 5 log₁₀(d / 10) and Type Ia supernovae standard candles. Finally, cosmological redshift (z = Δλ / λ ≈ v / c) and Hubble's Law (v = H₀d), alongside the 2.7 K Cosmic Microwave Background and primordial Helium-to-Hydrogen ratio, provide the three pillars of Big Bang cosmology.