Lists of data, formulae and relationships
Data
| Name of constant | Symbol and value |
|---|---|
| Gravitational contstant | $G = 6.67 \times 10^{-11} \text{N m}^2 \text{kg}^{-2}$ |
| Acceleration of free fall (close to earth) | $g = 9.81 \text{m s}^{-2}$ |
| Gravitational field strength (close to earth) | $g = 9.81 \text{N kg}^{-1}$ |
| Electronic charge | $e = -1.60 \times 10^{-19} \text{C}$ |
| Electronic mass | $m_e = 9.11 \times 10^{-31} \text{kg}$ |
| Electronvolt | $1 eV = 1.60 \times 10^{-19} \text{J}$ |
| Unified mass unit | $u = 1.66 \times 10^{-27} \text{kg}$ |
| Planck constant | $h = 6.63 \times 10^{-34} \text{J s}$ |
| Speed of light in a vacuum | $c = 3.00 \times 10^{8} \text{m s}^{-1}$ |
| Molar gas constant | $R = 8.31 \text{J K}^{-1} mol^{-1}$ |
| Boltzmann constant | $k = 1.38 \times 10^{-23} \text{J K}^{-1}$ |
| Avogadro constant | $N_A = 6.02 \times 10^{23} \text{mol}^{-1}$ |
| Permittivity of free space | $ \epsilon _{0} = 8.85 \times 10^{-12} \text{F} \text{m}^{-1}$ |
| Permeability of free space | $\mu _0 = 4\pi \times 10^{-7} \text{N} \text{A}^{-2}$ |
Mechanics
| Description | Formula |
|---|---|
| For uniformly accelerated motion | $v = u + at$ $s = ut + \frac{1}{2} at^2$ $v^2 = u^2 + 2as$ where $u$ = initial velocity, $v$ = final velocity, $s$ = distance, $t$ = time and $a$ = acceleration |
| Force | $F = \dfrac{\Delta p}{\Delta t}$ |
| Power | $P = Fv$ |
| Angular speed | $\omega = \dfrac{\Delta \theta}{\Delta t} = \dfrac{v}{r}$ where $r$ is the radius of the circular path |
| Period | $T = \dfrac{1}{f} = \dfrac{2\pi}{\omega}$ |
| Radial acceleration | $a = r\omega^2 = \dfrac{v^2}{r}$ |
Electricity
| Description | Formula |
|---|---|
| Electric current | $I = nAQv$ (Number of charge carriers per unit volume $n$) |
| Electric power | $P = I^2R$ |
| Terminal potential difference | $V = E - Ir$ (EMF $E$; Internal resistance $r$) |
| Resistors in series | $R = R_1 + R_2 + R_3$ |
| Resistors in parallel | $\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}$ |
| Capacitors in parallel | $C = C_1 + C_2 +C_3$ |
| Capacitors in series | $\dfrac{1}{C} = \dfrac{1}{C_1} + \dfrac{1}{C_2} + \dfrac{1}{C_3}$ |
| Energy stored | $W = \frac{1}{2}CV^2$ |
Nuclear physics
| Description | Formula |
|---|---|
| Mass-energy equivalence | $\Delta E = \Delta mc^2$ |
| Radioactive decay rate | $\dfrac{\delta N}{\delta t} = -\lambda N$ where $N$ = decay constant. $N = N_0e^{-\lambda t}$ |
| Half life | $t_{\frac{1}{2}} = \dfrac{\text{ln} 2}{\lambda}$ |
Quantum phenomena
| Description | Formula |
|---|---|
| Maximum energy of photoelectrons | $= hf - \phi$ where $\phi$ = Work function (J or eV) |
| Photon model | $E = hf$ |
| de Broglie wavelength | $\lambda = \dfrac{h}{p}$ |
Matter and materials
| Description | Formula |
|---|---|
| Density | $\rho = \dfrac{m}{V}$ |
| Hooke's law | $F = k\Delta x$ |
| Stress | $\sigma = \dfrac{F}{A}$ |
| Strain | $\epsilon = \dfrac{\Delta l}{l}$ |
| Young modulus | $E = \dfrac{\text{Stress}}{\text{Strain}}$ |
| Work done in stretching | $\Delta W = \frac{1}{2}F\Delta x$ (provided Hooke's law holds) |
Oscillations, waves and sinusoidal variations
| Description | Formula |
|---|---|
| For a simple pendulum | $T = 2\pi \sqrt{\dfrac{l}{g}}$ |
| For a mass on a spring | $T = 2\pi \sqrt{\dfrac{m}{k}}$ (where $k$ = a constant for the spring, stiffness) |
| Simple harmoic motion, acceleration | $a = -\omega^2x$ |
| At distance $r$ from a point source of power $P$, intensity | $I = \dfrac{P}{4\pi r^2}$ |
| For Young's slits, of slip separation $s$, wavelength | $\lambda = \dfrac{xs}{D}$ (where $x$ = fringe width and $D$ = slits t screen distance) |
| Refraction | $\dfrac{\text{sin}\theta_1}{\text{sin}\theta_2} = \dfrac{\lambda_1}{\lambda_2} = \dfrac{c_1}{c_2} = \dfrac{n_1}{n_2}$ where $n$ = refractive index. $\text{sin}\theta_c = \dfrac{c_1}{c_2}$ $n_1 = \dfrac{c}{c_1}$ |
| Simple harmonic motion | $\text{displacement} x = x_0 \text{sin} 2 \pi ft$ $\text{maximum speed} = 2\pi fx_0$ $\text{acceleration} a = -(2\pi f)^2 x$ |
| For $I = I_0 \text{sin} 2\pi ft$ and $V = V_0 \text{sin} 2\pi ft$: | $I_{rms} = \dfrac{I_0}{sqrt{2}}$ and $V_{rms} = \dfrac{V_0}{sqrt{2}}$ $\text{Mean power} = I_{rms} \times V_{rms} = \dfrac{I_0 V_0}{2}$ |
Thermal physics
| Description | Formula |
|---|---|
| Work done or energy transferred | $\Delta W = \Delta E + p\Delta V$ where $p$ = pressure and $V$ = volume. |
| Change of internal energy | $\Delta U = \Delta Q + \Delta W$ where $\Delta Q$ = energy transferred thermally and $\Delta W$ = work done on body. $\text{Energy transfer} = mc\Delta T$ where $c$ = specific heat capacity. $\text{Energy transfer} = l\Delta m$ where $l$ = specific latent heat or specific enthalpy change. |
| Rate of energy transfer by thermal conduction | $\dfrac{\Delta Q}{\Delta t} = kA \dfrac{\Delta T}{\Delta x}$ where $k$ = thermal conductivity and $\dfrac{\Delta T}{\Delta x}$ = thermal gradient. $\dfrac{\Delta Q}{\Delta t} = UA\Delta T$ |
| Kinetic theory | $pV = \frac{1}{3}Nm\langle c^2\rangle$ $T \propto \text{Average kinetic energy of molecules}$ |
| Mean kinetic energy of molecules | $= \frac{3}{2}kT$ where $k$ = Boltzmann constant. |
| Molar gas constant | $R = kN_A$ where $N_A$ = Avogadro contsant. |
| Pressure difference in fluid | $\Delta p = \rho g\Delta h$ Upthrust, $U$ = weight of displaced fluid. |
| For a heat engine, maximum efficiency | $= \dfrac{T_1 - T_2}{T_1}$ |
Fields
| Description | Formula |
|---|---|
| Electric field strength | $E = F/Q$ |
| for uniform field | $E = V/d$ |
| for radial field | $E = kQ/r^2$ where $k = 1/4\pi \epsilon_0$ for free space or air |
| Electrical potential for a radial field | $V = kQ/r$ |
| For an electron in a vacuum tube | $e\Delta V = \Delta (\frac{1}{2}m_ev^2)$ |
| Gravitational field strength | $g = F/m$ |
| for radial field | $g = Gm/r^2$, numerically |
| Gravitaional potential for a radial field | $V = -Gm/r$ |
| Capacitance of parallel plates | $C = \dfrac{\epsilon_0\epsilon_1A}{d}$ |
| Time constant for capacitor charge or discharge | $= RC$ |
| Force on a wire | $F = BIl$ |
| Force on a moving charge | $F = BQv$ |
| Field inside a long solenoid | $B = \mu_0nI$ where $n$ = number of turns per metre. |
| Field near a long straight wire | $B = \dfrac{\mu_0I}{2\pi r}$ |
| Magnetic flux | $\Phi = BA$ |
| EMF induced in a coil | $E = -\dfrac{Nd\Phi}{\delta t}$ where $N$ = number of turns. |
| EMF induced in a moving conductor | $E = Blv$ |
General geometry and mathematics
| Description | Formula |
|---|---|
| Surface area | $\text{cylinder} = 2\pi rh + 2\pi r^2$ $\text{sphere} = 4\pi r^2$ |
| Volume | $\text{cylinder} = \pi r^2h$ $\text{sphere} = \frac{4}{3}\pi r^3$ |
| For small angles | $\sin \theta \approx \tan \theta \approx \theta$ (in radians) $\cos \theta \approx 1$ |
Notes
The mathematical symbols in this page are produced using the MathJax open source JavaScript maths display engine for websites. This library turns LaTeX code into high quality, scalable typography. If formulae do not render correctly, check to see if JavaScript is enabled in your browser.
Published on 12th March 2013.
