Every equation in AQA A-level Physics (7408), the core sections 3.1 to 3.8 and all five options, has its own free page: key definitions, the equation with units, and 10 ramped questions from core to stretch, each with a full worked solution. Work on paper first, then open the solution.
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3.1 Measurements and their errors
- Combining Uncertainties: Adding, Multiplying and Powers (3.1.2)
- Uncertainties: Absolute, Fractional and Percentage (3.1.2)
3.2 Particles and radiation
- Specific Charge: Charge ÷ Mass (3.2.1.1)
- Annihilation and Pair Production: E = mc² (3.2.1.3)
- Photon Energy: E = hf = hc/λ (3.2.1.3)
- Photoelectric Effect: hf = φ + Ek(max) (3.2.2.1)
- Energy Levels: hf = E₁ − E₂ (3.2.2.3)
- de Broglie Wavelength: λ = h/mv (3.2.2.4)
3.3 Waves
- Phase Difference: φ = 2πd/λ (3.3.1.1)
- Wave Speed: c = fλ and f = 1/T (3.3.1.1)
- Stationary Waves: f = (1/2l)√(T/μ) (3.3.1.3)
- Young’s Double Slit: w = λD/s (3.3.2.1)
- Diffraction Grating: d sin θ = nλ (3.3.2.2)
- Critical Angle: sin θc = n₂/n₁ (3.3.2.3)
- Refractive Index: n = c/cₛ (3.3.2.3)
- Snell’s Law: n₁ sin θ₁ = n₂ sin θ₂ (3.3.2.3)
3.4 Mechanics and materials
- Moments: Moment = Fd (3.4.1.2)
- Uniform Acceleration: s = ut + ½at² (3.4.1.3)
- Uniform Acceleration: s = ½(u + v)t (3.4.1.3)
- Uniform Acceleration: v = u + at (3.4.1.3)
- Uniform Acceleration: v² = u² + 2as (3.4.1.3)
- Projectile Motion: suvat in Two Directions (3.4.1.4)
- Newton’s Second Law: F = ma (3.4.1.5)
- Impulse: FΔt = Δ(mv) (3.4.1.6)
- Momentum and Force: p = mv and F = Δ(mv)/Δt (3.4.1.6)
- Efficiency: efficiency = useful output power ÷ input power (3.4.1.7)
- Power: P = ΔW/Δt and P = Fv (3.4.1.7)
- Work Done: W = Fs cos θ (3.4.1.7)
- Kinetic and Potential Energy: Eₖ = ½mv² and ΔEₚ = mgΔh (3.4.1.8)
- Density: ρ = m/V (3.4.2.1)
- Elastic Strain Energy: E = ½FΔL (3.4.2.1)
- Hooke’s Law: F = kΔL (3.4.2.1)
- Stress, Strain and the Young Modulus: E = FL ÷ AΔL (3.4.2.2)
3.5 Electricity
- Current: I = ΔQ/Δt (3.5.1.1)
- Potential Difference: V = W/Q (3.5.1.1)
- Resistance: R = V/I (3.5.1.1, 3.5.1.2 and 3.5.1.3)
- Resistivity: ρ = RA/L (3.5.1.3)
- Electrical Power and Energy: P = VI = I²R = V²/R and E = VIt (3.5.1.4)
- Resistors in Series and Parallel: R_T = R₁ + R₂ + … and 1/R_T = 1/R₁ + 1/R₂ + … (3.5.1.4)
- Potential Dividers: Vout = Vin × R₂/(R₁ + R₂) (3.5.1.5)
- EMF and Internal Resistance: ε = E/Q and ε = I(R + r) (3.5.1.6)
3.6 Further mechanics and thermal physics
- Angular Speed: ω = v/r = 2πf (3.6.1.1)
- Centripetal Force: F = mv²/r = mω²r (3.6.1.1)
- SHM Acceleration: a = −ω²x (3.6.1.2)
- SHM Displacement: x = A cos ωt (3.6.1.2)
- SHM Velocity: v = ±ω√(A² − x²) (3.6.1.2)
- Mass–Spring System: T = 2π√(m/k) (3.6.1.3)
- Simple Pendulum: T = 2π√(l/g) (3.6.1.3)
- Specific Heat Capacity: Q = mcΔθ (3.6.2.1)
- Specific Latent Heat: Q = ml (3.6.2.1)
- Gas Laws: pV = constant, V/T = constant, p/T = constant (3.6.2.2)
- Ideal Gas Equation: pV = nRT and pV = NkT (3.6.2.2)
- Kinetic Theory: pV = ⅓Nm(crms)² and ½m(crms)² = (3/2)kT (3.6.2.3)
3.7 Fields and their consequences
- Newton’s Law of Gravitation: F = Gm₁m₂/r² (3.7.2.1)
- Gravitational Field Strength: g = F/m and g = GM/r² (3.7.2.2)
- Gravitational Potential: V = −GM/r (3.7.2.3)
- Orbits and Satellites: v = √(GM/r) and T² ∝ r³ (3.7.2.4)
- Coulomb’s Law: F = Q₁Q₂/(4πε₀r²) (3.7.3.1)
- Electric Field Strength: E = F/Q and E = Q/(4πε₀r²) (3.7.3.2)
- Uniform Electric Field: E = V/d (3.7.3.2)
- Electric Potential: V = Q/4πε₀r (3.7.3.3)
- Capacitance: C = Q/V (3.7.4.1)
- Parallel-Plate Capacitor: C = Aε₀εᵣ/d (3.7.4.2)
- Energy Stored by a Capacitor: E = ½QV (3.7.4.3)
- Capacitor Charging: Q = Q₀(1 − e^(−t/RC)) (3.7.4.4)
- Capacitor Discharge: Q = Q₀e^(−t/RC) (3.7.4.4)
- Force on a Current-Carrying Wire: F = BIl (3.7.5.1)
- Force on a Moving Charge: F = BQv (3.7.5.2)
- Magnetic Flux and Flux Linkage: Φ = BA (3.7.5.3)
- Electromagnetic Induction: ε = NΔΦ/Δt (3.7.5.4)
- Alternating Current: Irms = I0/√2 and Vrms = V0/√2 (3.7.5.5)
- Transformers: Ns/Np = Vs/Vp (3.7.5.6)
3.8 Nuclear physics
- Inverse-Square Law for Gamma: I = k/x² (3.8.1.2)
- Activity and Decay Constant: A = λN (3.8.1.3)
- Exponential Decay: N = N₀e^(−λt) (3.8.1.3)
- Half-Life: T½ = ln 2/λ (3.8.1.3)
- Nuclear Radius: R = R₀A^(1/3) (3.8.1.5)
- Binding Energy and Mass Defect: E = mc² (3.8.1.6)
3.9 Astrophysics (option)
- Angular Magnification: M = f₀/fₑ (3.9.1.1)
- Resolving Power: θ ≈ λ/D (3.9.1.4)
- Absolute Magnitude: m − M = 5 log(d/10) (3.9.2.2)
- Stefan’s Law: P = σAT⁴ (3.9.2.3)
- Wien’s Law: λmax T = 2.9 × 10⁻³ m K (3.9.2.3)
- Schwarzschild Radius: Rₛ ≈ 2GM/c² (3.9.2.6)
- Doppler Effect and Red Shift: z = Δf/f = v/c (3.9.3.1)
- Hubble’s Law: v = Hd (3.9.3.2)
3.10 Medical physics (option)
- Lens Power: P = 1/f (3.10.1.2)
- Thin Lens Equation: 1/f = 1/u + 1/v (3.10.1.2)
- Intensity Level: 10 log(I/I₀) (3.10.2.2)
- Acoustic Impedance: Z = ρc (3.10.4.1)
- X-ray Attenuation: I = I₀e^(−μx) (3.10.5.3)
- Effective Half-life: 1/T_E = 1/T_B + 1/T_P (3.10.6.2)
3.11 Engineering physics (option)
- Moment of Inertia: I = Σmr² (3.11.1.1)
- Rotational Kinetic Energy: Eₖ = ½Iω² (3.11.1.2)
- Rotational Motion: ω₂ = ω₁ + αt (3.11.1.3)
- Torque: T = Iα (3.11.1.4)
- Angular Momentum: L = Iω (3.11.1.5)
- Work and Power in Rotation: W = Tθ and P = Tω (3.11.1.6)
- First Law of Thermodynamics: Q = ΔU + W (3.11.2.1)
- Non-flow Processes: pV^γ = constant and W = pΔV (3.11.2.2)
- Engine Power: Indicated Power and P = Tω (3.11.2.4)
- Heat Engine Efficiency: W/Q_H and (T_H − T_C)/T_H (3.11.2.5)
- Heat Pumps and Refrigerators: COP (3.11.2.6)
3.12 Turning points in physics (option)
- Electron Gun: ½mv² = eV (3.12.1.2)
- Specific Charge of the Electron: e/m = v/(Br) (3.12.1.3)
- Millikan’s Oil Drop: QV/d = mg (3.12.1.4)
- Stokes’ Law: F = 6πηrv (3.12.1.4)
- Speed of Electromagnetic Waves: c = 1/√(μ₀ε₀) (3.12.2.3)
- Electron Wavelength: λ = h/√(2meV) (3.12.2.5)
- Time Dilation: t = t₀/√(1 − v²/c²) (3.12.3.3)
- Length Contraction: l = l₀√(1 − v²/c²) (3.12.3.4)
- Mass and Energy: E = mc² = m₀c²/√(1 − v²/c²) (3.12.3.5)
3.13 Electronics (option)
- Sampling and Bit Rate (3.13.2.1)
- LC Resonant Filter: f₀ = 1/(2π√(LC)) (3.13.3.1)
- Q Factor: Q = f₀/f_B (3.13.3.1)
- Op-amp Comparator: V_out = A_OL(V₊ − V₋) (3.13.3.2)
- Inverting Amplifier: V_out/V_in = −R_f/R_in (3.13.4.1)
- Non-inverting Amplifier: V_out/V_in = 1 + R_f/R₁ (3.13.4.2)
- Difference Amplifier: V_out = (V₊ − V₋)R_f/R₁ (3.13.4.3)
- Summing Amplifier: V_out = −R_f(V₁/R₁ + V₂/R₂ + …) (3.13.4.3)
- Op-amp Gain × Bandwidth = Constant (3.13.4.4)