Physics A Data Sheet - A-Levels Physics

5c. Physics A data sheet

Data, Formulae and Relationships

The data, formulae and relationships in this data sheet will be printed for distribution with the examination papers.

Values are given to three significant figures, except where more - or fewer - are useful.

Quantity	Conversion
Unified atomic mass unit	$1\,\mathrm{u} = 1.661 \times 10^{-27}\,\mathrm{kg}$
Electronvolt	$1\,\mathrm{eV} = 1.60 \times 10^{-19}\,\mathrm{J}$
Day	$1\,\mathrm{day} = 8.64 \times 10^4\,\mathrm{s}$
Year	$1\,\mathrm{year} \approx 3.16 \times 10^7\,\mathrm{s}$
Light year	$1\,\mathrm{light\ year} \approx 9.5 \times 10^{15}\,\mathrm{m}$
Parsec	$1\,\mathrm{parsec} \approx 3.1 \times 10^{16}\,\mathrm{m}$

Relationship	Equation
Arc length	$s = r\theta$
Circumference of circle	$C = 2\pi r$
Area of circle	$A = \pi r^2$
Curved surface area of cylinder	$A = 2\pi rh$
Surface area of sphere	$A = 4\pi r^2$
Area of trapezium	$A = \frac{1}{2}(a + b)h$
Volume of cylinder	$V = \pi r^2h$
Volume of sphere	$V = \frac{4}{3}\pi r^3$
Pythagoras' theorem	$a^2 = b^2 + c^2$
Cosine rule	$a^2 = b^2 + c^2 - 2bc\cos A$
Sine rule	$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
Small angle approximations	$\sin\theta \approx \tan\theta \approx \theta$ and $\cos\theta \approx 1$
Logarithm product rule	$\log(AB) = \log(A) + \log(B)$
Logarithm quotient rule	$\log\left(\frac{A}{B}\right) = \log(A) - \log(B)$
Logarithm power rule	$\log(x^n) = n\log(x)$
Natural logarithm	$\ln(e^{kx}) = kx$

Note: $\lg = \log_{10}$ and $\ln = \log_e$.

Topic	Formulae
Vectors	$F_x = F\cos\theta$ $F_y = F\sin\theta$

Topic	Formulae
Uniformly accelerated motion	$v = u + at$ $s = \frac{1}{2}(u + v)t$ $s = ut + \frac{1}{2}at^2$ $v^2 = u^2 + 2as$
Force	$F = \frac{\Delta p}{\Delta t}$ $p = mv$
Turning effects	$\text{moment} = Fx$ $\text{torque} = Fd$
Density	$\rho = \frac{m}{V}$
Pressure	$p = \frac{F}{A}$ $p = h\rho g$
Work, energy and power	$W = Fx\cos\theta$ $\text{efficiency} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\%$ $P = \frac{W}{t}$ $P = Fv$
Springs and materials	$F = kx$ $E = \frac{1}{2}Fx$ ; $E = \frac{1}{2}kx^2$ $\sigma = \frac{F}{A}$ $\varepsilon = \frac{x}{L}$ $E = \frac{\sigma}{\varepsilon}$

Topic	Formulae
Charge	$\Delta Q = I\Delta t$
Current	$I = Anev$
Work done	$W = VQ$ ; $W = \mathcal{E}Q$ ; $W = VIt$
Resistance and resistors	$R = \frac{\rho L}{A}$ $R = R_1 + R_2 + \cdots$ $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots$
Power	$P = VI$ , $P = I^2R$ and $P = \frac{V^2}{R}$
Internal resistance	$\mathcal{E} = I(R + r)$ ; $\mathcal{E} = V + Ir$
Potential divider	$V_{out} = \frac{R_2}{R_1 + R_2} \times V_{in}$ $\frac{V_1}{V_2} = \frac{R_1}{R_2}$
Waves	$v = f\lambda$ $f = \frac{1}{T}$ $I = \frac{P}{A}$ $\lambda = \frac{ax}{D}$
Refraction	$n = \frac{c}{v}$ $n\sin\theta = \text{constant}$ $n_1\sin\theta_1 = n_2\sin\theta_2$ $\sin C = \frac{1}{n}$
Quantum physics	$E = hf$ ; $E = \frac{hc}{\lambda}$ $hf = \phi + KE_{max}$ $\lambda = \frac{h}{p}$

Topic	Formulae
Thermal physics	$E = mc\Delta\theta$ $E = ml$
Ideal gases	$pV = NkT$ ; $pV = nRT$ $pV = \frac{1}{3}Nm\overline{c^2}$ $\frac{1}{2}m\overline{c^2} = \frac{3}{2}kT$ $E = \frac{3}{2}kT$
Circular motion	$\omega = \frac{2\pi}{T}$ ; $\omega = 2\pi f$ $v = \omega r$ $a = \frac{v^2}{r}$ ; $a = \omega^2r$ $F = \frac{mv^2}{r}$ ; $F = m\omega^2r$
Oscillations	$\omega = \frac{2\pi}{T}$ $a = -\omega^2x$ $x = A\cos\omega t$ ; $x = A\sin\omega t$ $v = \pm\omega\sqrt{A^2 - x^2}$
Gravitational field	$g = \frac{F}{m}$ $F = -\frac{GMm}{r^2}$ $g = -\frac{GM}{r^2}$ $T^2 = \left(\frac{4\pi^2}{GM}\right)r^3$ $V_g = -\frac{GM}{r}$ $\text{energy} = -\frac{GMm}{r}$
Astrophysics	$hf = \Delta E$ ; $\frac{hc}{\lambda} = \Delta E$ $d\sin\theta = n\lambda$ $\lambda_{max} \propto \frac{1}{T}$ $L = 4\pi r^2\sigma T^4$
Cosmology	$\frac{\Delta\lambda}{\lambda} \approx \frac{\Delta f}{f} \approx \frac{v}{c}$ $p = \frac{1}{d}$ $v = H_0d$ $t = H_0^{-1}$

Topic	Formulae
Capacitance and capacitors	$C = \frac{Q}{V}$ $C = \frac{\varepsilon_0A}{d}$ $C = 4\pi\varepsilon_0R$ $C = C_1 + C_2 + \cdots$ $\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots$ $W = \frac{1}{2}QV$ ; $W = \frac{1}{2}\frac{Q^2}{C}$ ; $W = \frac{1}{2}CV^2$ $\tau = CR$ $x = x_0e^{-t/CR}$ $x = x_0(1 - e^{-t/CR})$
Electric field	$E = \frac{F}{q}$ $F = \frac{Qq}{4\pi\varepsilon_0r^2}$ $E = \frac{Q}{4\pi\varepsilon_0r^2}$ $E = \frac{V}{d}$ $V = \frac{Q}{4\pi\varepsilon_0r}$ $\text{energy} = \frac{Qq}{4\pi\varepsilon_0r}$
Magnetic field	$F = BIL\sin\theta$ $F = BQv$
Electromagnetism	$\Phi = BA\cos\theta$ $\mathcal{E} = -\frac{\Delta(N\Phi)}{\Delta t}$ $\frac{N_s}{N_p} = \frac{V_s}{V_p} = \frac{I_p}{I_s}$
Radius of nucleus	$R = r_0A^{1/3}$
Radioactivity	$A = \lambda N$ ; $\frac{\Delta N}{\Delta t} = -\lambda N$ $\lambda t_{1/2} = \ln(2)$ $A = A_0e^{-\lambda t}$ $N = N_0e^{-\lambda t}$
Einstein's mass-energy equation	$\Delta E = \Delta mc^2$
Attenuation of X-rays	$I = I_0e^{-\mu x}$
Ultrasound	$Z = \rho c$ $\frac{I_r}{I_0} = \left(\frac{Z_2 - Z_1}{Z_2 + Z_1}\right)^2$ $\frac{\Delta f}{f} = \frac{2v\cos\theta}{c}$