H2 Physics Formula List
Revise H2 Physics 9478 equations with symbols, units, sign conventions, assumptions and short application checks.
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A topic-organised equation reference for H2 Physics (9478, 2027). Each row pairs a relationship with its symbols, units and model conditions. This is a learning reference; check the official examination data sheet to see which relationships are supplied.
Choose the model before the equation
Identify the system, choose positive directions, and decide what stays constant. Check units and limiting cases after calculating. E may mean energy or electric field; p may mean momentum or pressure; ρ may mean density or resistivity. Read the local definitions.
Common data and conversions
These are typical rounded values for revision. Use the data supplied with your examination or question when it differs.
| Quantity | Symbol | Typical value |
|---|---|---|
| Free-fall acceleration near Earth’s surface | g | 9.81 m s⁻² |
| Speed of light in vacuum | c | 3.00 × 10⁸ m s⁻¹ |
| Elementary charge | e | 1.60 × 10⁻¹⁹ C |
| Planck constant | h | 6.63 × 10⁻³⁴ J s |
| Gravitational constant | G | 6.67 × 10⁻¹¹ N m²kg⁻² |
| Boltzmann constant | k | 1.38 × 10⁻²³ J K⁻¹ |
| Molar gas constant | R | 8.31 J mol⁻¹K⁻¹ |
| Avogadro constant | N_A | 6.02 × 10²³ mol⁻¹ |
| Permittivity of free space | ε₀ | 8.85 × 10⁻¹² F m⁻¹ |
| Permeability of free space | μ₀ | Approximately 4π × 10⁻⁷ H m⁻¹ |
Quantities, uncertainty and vectors
| Relationship | Symbols and units | When to use it |
|---|---|---|
| fractional uncertainty = Δ x/| x| | Absolute uncertainty Δ x has the unit of x | Multiply by 100% for percentage uncertainty. |
| Δ z = Δ x + Δ y for z = x± y | Absolute uncertainties in compatible units | Estimate the maximum combined uncertainty for sums or differences. |
| Δ z/| z| = | a|Δ x/| x| + | b|Δ y/| y| for z = x^a y^b | Fractional uncertainties have no unit | Small-uncertainty estimate; add contributions even when an exponent is negative. |
| Fₓ = F cos θ, F_y = F sin θ | Components in N | θ is measured from the positive x direction; assign signs from the diagram. |
Use SI base units for dimensional checks. A consistent equation is necessary, but dimensional consistency alone cannot prove a model correct. Common conversions: 1 eV = 1.60 × 10⁻¹⁹ J, 1 u = 1.66 × 10⁻²⁷ kg, and 1 kW h = 3.60 × 10⁶ J. Use the numerical constants supplied in the question for your final answer.
Forces, motion and projectiles
| Relationship | Symbols and units | When to use it |
|---|---|---|
| v = ds/dt; a = dv/dt; Δ s = ∫ v dt | Velocity m/s; acceleration m s⁻²; displacement m | Signed gradients and area; also apply to non-uniform acceleration. |
| ∑ F = 0; ∑ M = 0; W = mg | Force N; moment N m; mass kg | Translational and rotational equilibrium; weight uses local g. |
| F = kx | Spring constant k in N m⁻¹; extension x in m | Magnitude of restoring force within the limit of proportionality; signed form is F = -kx about equilibrium. |
| M = Fd_⊥; τ_couple = Fd | Moment/torque in N m | d_⊥ is pivot-to-line distance; for a couple, d is separation of the parallel force lines. |
| Fᵣₑₛᵤₗₜₐₙₜ = ma | Force N; mass kg; acceleration m s⁻² | Constant mass; choose the system before adding forces. |
| v = u + at; s = ut + (1/2)at² | u,v in m s⁻¹; s in m; t in s | Straight-line motion with constant acceleration. |
| v² = u² + 2as; s = (1/2)(u + v)t | Signed displacement and velocities | Same constant-acceleration model; useful when time or acceleration is absent. |
| x = u cos θ t; y = u sin θ t-(1/2)gt² | Position relative to launch point in m | Projectile, no drag, uniform g, horizontal x and upward y. |
| range = u² sin(2θ)/g | Range in m | Derived result: launch and landing at the same height; no drag. |
Momentum, collisions and energy
| Relationship | Symbols and units | When to use it |
|---|---|---|
| p = mv; F = Δ p/Δ t | Momentum p in kg m s⁻¹ | Force form gives average resultant force over the interval. |
| J = Δ p = ∫ F dt | Impulse J in N s | Signed area under the resultant force–time graph; for constant force, J = FΔ t. |
| ∑ p_before = ∑ p_after | Use signed velocities along one chosen axis | Negligible net external impulse on the system; kinetic energy need not be conserved. |
| u₁-u₂ = -(v₁-v₂) | Relative velocities in m s⁻¹ | One-dimensional elastic collision; use alongside momentum conservation. |
| W = Fs cos θ | Work J; displacement m | Constant force; θ is angle between force and displacement. |
| Eₖ = (1/2)mv²; E_elastic = (1/2)kx² | Energy J | Elastic form assumes Hooke’s law; generally use area under force–extension graph. |
| Δ U = -W_field; Δ U_g = mgΔ h | Potential-energy change J | Uniform gravity for the second form; rising increases U_g. |
| P = E/t; P = Fv cos θ | Power W | First is average power; second is instantaneous mechanical power. |
| η = P_useful/Pᵢₙₚᵤₜ | No unit | May also use energies; percentage efficiency is 100η%. |
Circular motion and gravitation
| Relationship | Symbols and units | When to use it |
|---|---|---|
| θ = s/r; ω = Δθ/Δ t | θ in rad; ω in rad s⁻¹ | s is arc length, not a chord. |
| ω = 2π/T; v = rω | Period T in s; radius r in m | Uniform circular motion. |
| a_c = v²/r = rω² | Centripetal acceleration m s⁻² | Directed towards the centre even when speed is constant. |
| F_c = mv²/r = mrω² | Resultant radial force N | “Centripetal” names the resultant, not an additional force. |
| F_g = GMm/r²; g = GM/r² | G in N m²kg⁻²; g in N kg⁻¹ | Point masses or outside a spherically symmetric mass; r is centre-to-centre distance. |
| v_orbit = square root of (GM/r); T² = 4π²r³/(GM) | Orbital speed m s⁻¹; period s | Circular orbit around dominant mass M; gravity supplies the radial force. |
Gravitational potential and orbits
| Relationship | Symbols and units | When to use it |
|---|---|---|
| φ = -GM/r; U = mφ = -GMm/r | Potential φ in J/kg; U in J | Zero potential at infinity; outside a spherical source. A nearer point has more negative potential. |
| g = -dφ/dr | Radial field component in N/kg | Positive radial direction is outwards; gravitational field points inwards. |
| E_orbit = -GMm/(2r) | Total orbital energy J | Circular orbit: add (1/2)mv² to gravitational potential energy. |
| v_escape = square root of (2GM/r) | Speed m/s | Minimum escape speed with zero final speed at infinity; no drag or further propulsion. |
Oscillations
| Relationship | Symbols and units | When to use it |
|---|---|---|
| a = -ω²x; x = A cos(ω t + φ) | Displacement/amplitude m; phase φ rad | Simple harmonic motion about equilibrium; acceleration opposes displacement. |
| v = ±ω square root of (A²-x²); vₘₐₓ = ω A | Velocity/speed m/s | Choose the velocity sign from motion direction. |
| T = 2π/ω; E = (1/2)mω²A² | Period s; total energy J | Undamped SHM; Eₚ = (1/2)mω²x² and Eₖ = E-Eₚ. |
| T_spring = 2π square root of (m/k); T_pendulum = 2π square root of (l/g) | k in N/m; length l in m | Ideal spring with negligible spring mass; simple pendulum at small angle. |
Waves, superposition and polarisation
| Relationship | Symbols and units | When to use it |
|---|---|---|
| v = fλ; f = 1/T | Speed m/s; wavelength m; frequency Hz | Progressive wave; speed and wavelength refer to the same medium. |
| Δφ = 2πΔ x/λ | Phase difference rad | Spatial phase comparison at one time; time comparison uses 2πΔ t/T. |
| I = P/A; I ∝ A_wave² | Intensity W/m² | Same medium and wave frequency for amplitude comparisons. |
| I = P/(4π r²) | Source distance r in m | Isotropic point source, no absorption; inverse-square spreading. |
| I = I₀ cos² θ | Intensity W/m² | Malus’ law: incident plane-polarised light; θ between its polarisation and analyser axis. |
| Δ x = nλ; Δ x = (n + 1/2)λ | Path difference m; integer n | Constructive / destructive interference for coherent sources initially in phase. |
| w = λ D/a | Fringe spacing w, slit separation a, screen distance D in m | Young’s double slit; small angles, D much larger than a. |
| d sin θ = nλ | Grating spacing d in m; integer order n | Diffraction grating at normal incidence; | nλ/d| ≤ 1. |
| fₙ = nv/(2L) | Frequency Hz; vibrating length L m | String fixed at both ends, or ideal pipe open at both ends. |
| fₙ = (2n-1)v/(4L) | Positive integer n | Ideal pipe closed at one end; odd harmonics only, neglect end correction. |
Temperature, gases and thermodynamics
| Relationship | Symbols and units | When to use it |
|---|---|---|
| T/K = θ/°C + 273.15 | Thermodynamic temperature T in K | Use absolute temperature in gas equations. |
| pV = NkT = nRT; N = nN_A | Pressure Pa; volume m³; particle count N; amount n mol | Ideal gas; k in J/K, R in J/(mol K), N_A in mol⁻¹. |
| pV = (1/3)Nm⟨v²⟩; (1/2)m⟨v²⟩ = (3/2)kT | Particle mass m kg; mean square speed ⟨v²⟩ | Ideal-gas kinetic model; do not confuse mean speed with root mean square speed. |
| U = (3/2)NkT | Internal energy J | Monatomic ideal gas with only translational contributions. |
| Δ U = Q + Wₒₙ; Wₒₙ = -pΔ V | Energy and work J | First law; constant external pressure for the work formula. Compression gives positive work on the gas. |
| Q = mcΔ T; Q = ml | c in J/(kg K); l in J/kg | Temperature change without phase change / phase change without temperature change. |
Currents and circuits
| Relationship | Symbols and units | When to use it |
|---|---|---|
| I = Δ Q/Δ t; I = nAqv_d | Charge C; area m²; carrier density n in m⁻³; drift speed v_d in m/s | Magnitudes for a uniform conductor; use carrier charge magnitude q. |
| V = W/Q; ε = W_supplied/Q | p.d. and e.m.f. in V | Component energy transfer versus source energy supply per unit charge. |
| R = V/I; R = ρ l/A | Resistance Ω; resistivity ρ in Ω m | Uniform wire; resistivity depends on material and temperature. |
| Rₛ = ∑ Rᵢ; 1/Rₚ = ∑ 1/Rᵢ | Equivalent resistance Ω | Series: same current. Parallel: same p.d. |
| Vₜₑᵣₘᵢₙₐₗ = ε-Ir; I = ε/(R + r) | Internal resistance r and external resistance R in Ω | Cell delivering current; one external resistive load in the second form. |
| Vₒᵤₜ = VₛR₂/(R₁ + R₂) | Output p.d. V | Across R₂ in an unloaded divider; loading changes the effective resistance. |
| P = VI = I²R = V²/R; E = Pt | W, V, A, Ω, J and s | Use matching component quantities; E = Pt assumes constant power. |
Electric and magnetic forces
| Relationship | Symbols and units | When to use it |
|---|---|---|
| E = F/q; F = qE | Electric field E in N C⁻¹ | Vector equation: a negative charge experiences force opposite to the field. |
| E = V/d | Field in V m⁻¹; plate separation d in m | Magnitude in a uniform field between parallel plates, away from edges. |
| F = BIl sin θ | Flux density B in T; length l in m | Uniform magnetic field; θ is angle between current and field. |
| F = B| q| v sin θ | Magnetic force magnitude N | Moving charge; force is perpendicular to velocity and field, reversing for negative charge. |
| r = m v/(| q| B) | Orbit radius m | Non-relativistic particle moving perpendicular to a uniform magnetic field. |
| v = E/B | Selected speed m/s | Crossed fields with electric and magnetic forces opposite and equal. |
Electric potential, capacitors and RC circuits
| Relationship | Symbols and units | When to use it |
|---|---|---|
| F = Qq/(4πε₀r²); E = Q/(4πε₀r²) | Force N; radial field N/C | Point or spherical charge in vacuum; sign determines direction with outward positive. |
| V = Q/(4πε₀r); U = qV | Electric potential V; energy J | Zero at infinity; include charge sign. |
| E = -dV/dr | Radial field in V/m | Field points towards decreasing potential. |
| C = Q/V; U = (1/2)QV = (1/2)CV² = Q²/(2C) | Capacitance C/V = F | Q is charge magnitude on one plate; fixed capacitance. |
| Cₚ = ∑ Cᵢ; 1/Cₛ = ∑1/Cᵢ | Equivalent capacitance F | Parallel: same voltage. Series: same charge magnitudes for initially uncharged capacitors. |
| τ = RC; Q = Q₀e^(-t/τ) | Time constant s | Discharge through a fixed resistor; voltage and current magnitude also decay exponentially. |
| Q = Cε(1-e^(-t/RC)); I = (ε/R)e^(-t/RC) | Charge C; current A | Initially uncharged capacitor, ideal d.c. source and series resistor. |
Magnetic fields, induction and alternating current
| Relationship | Symbols and units | When to use it |
|---|---|---|
| B = μ₀I/(2π r) | Flux density T; distance r m | Long straight wire in air/vacuum. |
| B = μ₀NI/(2r); B = μ₀nI | Turns N; turns per metre n | At centre of a thin circular coil / inside a long solenoid in air/vacuum. |
| Φ = BA cos θ; Ψ = NΦ | Flux Φ in Wb; linkage Ψ in Wb turns | Uniform field; angle measured between field and area normal. |
| ε = -dΨ/dt | Induced e.m.f. V | Faraday’s law with Lenz’s sign; for a finite interval use the average rate of change. |
| ε₀ = NBAω | Peak e.m.f. V | Uniformly rotating coil in a uniform field; ε = ε₀ sin ω t with a suitable phase origin. |
| Vₚ/Vₛ = Nₚ/Nₛ; VₚIₚ = VₛIₛ | Matching voltage/current conventions | Ideal transformer; power equality for ideal resistive loads. |
| Iᵣₘₛ = I₀/square root of 2; Vᵣₘₛ = V₀/square root of 2 | A and V | Sinusoidal current/voltage; 0 denotes peak value. |
| P bar = Iᵣₘₛ²R = Vᵣₘₛ²/R | Mean power W | Pure resistor; no reactive phase shift. |
Quantum physics
| Relationship | Symbols and units | When to use it |
|---|---|---|
| E = hf = hc/λ; p = h/λ | Photon energy J; momentum kg m/s | Photon wavelength in vacuum. |
| hf = φ + Kₘₐₓ; Kₘₐₓ = eVₛ | Work function φ J; stopping p.d. Vₛ V | Photoelectric emission needs hf ≥ φ. |
| λ = h/p | de Broglie wavelength m | Matter wave; for a non-relativistic particle, p = mv. |
| Δ x Δ p≳ h | Position spread m; momentum spread kg m/s | Syllabus order-of-magnitude uncertainty estimate, not an exact numerical equality. |
| Eₙ = n²h²/(8mL²) | Energy J; box width L m; integer n ≥ 1 | One-dimensional infinite square well; zero potential inside. |
| Δ E = hf; P(a ≤ x ≤ b) = ∫ₐ^b|ψ|² dx | Energy difference J; probability has no unit | Spectral transition / normalised one-dimensional wavefunction; ∫|ψ|²dx = 1. |
Nuclear physics
| Relationship | Symbols and units | When to use it |
|---|---|---|
| N/N₀ = (1/2)^(t/t_(1/2)) | Half-life t_(1/2) in the same time unit as t | Repeated halving; also applies to activity of one radioactive isotope. |
| E = mc²; E_b = Δ m c² | Energy J; mass and mass defect kg | Binding energy from mass defect; keep atomic/nuclear mass accounting consistent. |
| E_released = (m_before-m_after)c² | Reaction energy J | Positive when products have lower total rest mass; count all reaction products. |
Exponential nuclear decay
| Relationship | Symbols and units | When to use it |
|---|---|---|
| A = λ N; N = N₀e^(-λ t) | Activity A in Bq; decay constant λ in s⁻¹ | One isotope with no replenishment; activity follows the same exponential. |
| t_(1/2) = ln 2/λ | Half-life s when λ is in s⁻¹ | Subtract background from detector count rates before fitting or comparing. |
A quick application: the direction of acceleration
A body has u = +6.0 m s⁻¹ and v = -2.0 m s⁻¹ after 4.0 s of constant acceleration. Then a = (v-u)/t = (-2.0-6.0)/4.0 = -2.0 m s⁻². The displacement is s = (1/2)(u + v)t = 8.0 m.
The body reverses direction during the interval. Its signed displacement is not its total distance, and negative acceleration does not mean slowing down throughout the motion.
Scope and next step
For fields and circuits, keep direction and signs separate from force or current magnitudes. For gases and oscillations, check the approximation before using a convenient derived result.
Use the course hub to find the lesson behind a relationship, then try its topic check with the reference closed.