# Lists of data, formulae and relationships

## Data

Name of constantSymbol 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

DescriptionFormula
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

DescriptionFormula
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

DescriptionFormula
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

DescriptionFormula
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

DescriptionFormula
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

DescriptionFormula
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

DescriptionFormula
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

DescriptionFormula
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

DescriptionFormula
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

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Published on 12th March 2013.