Physics Formula Sheet

Section A — Mechanics

Measurement

$\rho = \frac{m}{V}$

Density $\rho$ (kg m⁻³), mass $m$ (kg), volume $V$ (m³).

Vectors

$R = \sqrt{(F_1)^2 + (F_2)^2} \qquad \theta = \tan^{-1}\!\left(\frac{F_2}{F_1}\right)$

Resultant of two perpendicular forces; $\theta$ measured from $F_1$.

$F_x = F\cos\theta \qquad F_y = F\sin\theta$

Resolving a force $F$ at angle $\theta$ to the horizontal into components.

Statics

$T = Fd$

Moment $T$ (N m), force $F$ (N), perpendicular distance $d$ (m).

$F = ke$

Hooke's Law: force $F$ (N), spring constant $k$ (N m⁻¹), extension $e$ (m). Valid up to the elastic limit only.

$W = mg$

Weight $W$ (N), mass $m$ (kg), gravitational field strength $g = 10$ N kg⁻¹.

Motion

$v = u + at \qquad s = ut + \tfrac{1}{2}at^2 \qquad v^2 = u^2 + 2as \qquad s = \tfrac{1}{2}(u + v)t$

SUVAT equations for uniform acceleration. All four assume constant $a$.

$F = ma$

Newton's Second Law: net force $F$ (N), mass $m$ (kg), acceleration $a$ (m s⁻²).

$p = mv$

Momentum $p$ (kg m s⁻¹), mass $m$ (kg), velocity $v$ (m s⁻¹). Momentum is conserved in a closed system.

$F\Delta t = \Delta(mv)$

Impulse equals change in momentum. Force $F$ (N), time $\Delta t$ (s).

Energy, Work and Power

$W = Fd$

Work done $W$ (J), force $F$ (N), displacement $d$ (m) in the direction of the force.

$E_p = mgh \qquad E_k = \tfrac{1}{2}mv^2$

Gravitational potential energy and kinetic energy (J).

$P = \frac{E}{t}$

Power $P$ (W), energy $E$ (J), time $t$ (s).

$\text{efficiency} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\%$

Hydrostatics

$P = \frac{F}{A}$

Pressure $P$ (Pa), force $F$ (N), area $A$ (m²).

$\Delta P = \rho g \Delta h$

Fluid pressure at depth $\Delta h$ (m); fluid density $\rho$ (kg m⁻³), $g = 10$ N kg⁻¹.

$U = \rho_{\text{fluid}} \, g \, V_{\text{displaced}}$

Upthrust (Archimedes): buoyant force equals weight of fluid displaced.

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Section B — Thermal Physics

$T(\text{K}) = \theta(°\text{C}) + 273$

Kelvin to Celsius conversion. Absolute zero = 0 K = −273 °C.

$P_1 V_1 = P_2 V_2$

Boyle's Law (constant temperature).

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Charles' Law (constant pressure). Temperature must be in kelvin.

$\frac{P_1}{T_1} = \frac{P_2}{T_2}$

Pressure Law (constant volume). Temperature must be in kelvin.

$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

General gas law. Temperature must be in kelvin.

$E_H = mc\Delta\theta$

Specific heat capacity: thermal energy $E_H$ (J), mass $m$ (kg), specific heat capacity $c$ (J kg⁻¹ K⁻¹), temperature change $\Delta\theta$ (K or °C).

$E_H = mL$

Specific latent heat: thermal energy $E_H$ (J), mass $m$ (kg), specific latent heat $L$ (J kg⁻¹).

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Section C — Waves and Optics

$v = f\lambda \qquad f = \frac{1}{T}$

Wave equation: speed $v$ (m s⁻¹), frequency $f$ (Hz), wavelength $\lambda$ (m), period $T$ (s).

$d = \frac{vt}{2}$

Echo distance: total time $t$ (s), speed of sound $v \approx 330$ m s⁻¹. Factor of 2 because sound travels to reflector and back.

$n = \frac{\sin i}{\sin r}$

Snell's Law: refractive index $n$, angle of incidence $i$, angle of refraction $r$. Angles measured from the normal.

$n = \frac{c}{v}$

Refractive index in terms of wave speeds: speed of light in vacuum $c = 3 \times 10^8$ m s⁻¹, speed in medium $v$.

$n = \frac{\text{real depth}}{\text{apparent depth}}$

Real and apparent depth relationship for a flat surface.

$\sin C = \frac{1}{n}$

Critical angle $C$ for total internal reflection. TIR occurs when $i > C$ and light travels from denser to less dense medium.

$m = \frac{v}{u} \qquad \frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

Lens magnification and lens formula: image distance $v$, object distance $u$, focal length $f$. All distances measured from the optical centre; real distances are positive.

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Section D — Electricity and Magnetism

$I = \frac{Q}{t}$

Current $I$ (A), charge $Q$ (C), time $t$ (s).

$R = \frac{V}{I}$

Resistance $R$ (Ω), potential difference $V$ (V), current $I$ (A).

$R_s = R_1 + R_2 + R_3 + \cdots$

Series circuit: resistances add directly.

$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots$

Parallel circuit: reciprocals add.

$P = IV = I^2 R = \frac{V^2}{R}$

Electrical power $P$ (W). Choose the form that matches the given quantities.

$E = Pt$

Electrical energy $E$ (J), power $P$ (W), time $t$ (s).

$1 \text{ kWh} = 3.6 \times 10^6 \text{ J}$

Unit conversion for electricity bills.

$\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}$

Transformer ratios: secondary/primary voltage, turns, and current. For an ideal transformer: $V_p I_p = V_s I_s$.

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Section E — Physics of the Atom

$A = Z + N$

Mass number $A$ equals proton number $Z$ plus neutron number $N$.

$\Delta E = \Delta m c^2$

Mass-energy equivalence: energy released $\Delta E$ (J), mass deficit $\Delta m$ (kg), $c = 3 \times 10^8$ m s⁻¹.

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Constants and Values

FLASHCARD SET • 28 CARDSPhysics Formulae: Quick Recall