Page 1: Fundamental constants

Gravity acceleration g 9.81 ms^-2

Gravitational constant G 6.67 x 10^-11 Nm²kg^-2

Avogadro's constant N_A 6.02 x 10²³ mol^-1

Gas constant R 8.31 JK^-1 mol^-1

Boltzmann's constant k 1.38 x 10^-23 JK^-1

Stefan-Boltzmann constant s 5.67 x 10^-8 Wm^-2K^-4

Coulomb constant k 8.99 x 10⁹ Nm²C^-2

Permittivity of free space e₀ 8.85 x 10^-12 C²N^-1m^-2

Permeability of free space m₀ 4p x 10^-7 TmA^-1

Speed of light in vacuum c 3.00 x 10⁸ ms^-1

Planck's constant h 6.63 x 10^-34 Js

Charge on electron e 1.60 x 10^-19 C

Electron rest mass m_e 9.11 x 10^-31 kg = 0.000549 u = 0.511 MeV/c²

Proton rest mass m_p 1.673 x 10^-27 kg = 1.007276 u = 938 MeV/c²

Neutron rest mass mn 1.675 x 10^-27 kg = 1.008665 u = 940 MeV/c²

Unified atomic mass unit u 1.661 x 10^-27 kg = 931.5 MeV/c²

Page 2 : SI prefixes and unit conversions

tera = T = 10¹², giga = G = 10⁹, mega = M = 10⁶, kilo = k =10³, hecto = h = 10², deca = da = 10¹, deci = d = 10^-1, centi = c = 10^-2, milli = m = 10^-3, micro = m = 10^-6, nano = n = 10^-9, pico = p = 10^-12, femto = f = 10^-15

1 light year (ly) = 9.46 x 10¹⁵ m 1 parsec = 3.26 ly

1 astronomical unit(AU) = 1.50 x 10¹¹ m 1 radian (rad) = 180^o/p

1 kilowatt-hour (kWh) = 3.60 x 10⁶ J 1 atm = 1.01 x 10⁵ Nm^-2 =101 kPa = 760 mmHg

Page 3 : Electrical circuit symbols

Symbols are given for: cell, battery, lamp, ac supply, switch, ammeter, voltmeter, galvanometer, resistor, potentiometer, transformer, heating element

Page 4 : Measurement and mechanics

Horizontal and vertical components of the vector A: A_H = Acosq A_V = Asinq

Uncertainties: If y = a ± b then Dy = Da + Db

If y = ab/c then Dy/y = Da/a + Db/b + Dc/c

v = Ds/Dt a = Dv/Dt g = F/m g = Gm/r²

Page 5 : Mechanics

v = u + at s = ((u+v)/2)t s = ut + ½at² v² = u² + 2as

s : displacement, t : time, u : initial speed, v : final speed, a : acceleration

F = ma p =mv F = Dp/Dt E_k = p² / 2m

Impulse = FDt = Dp W = (F_ss =) Fs cosq E_k = ½mv² E_p = mgh

P (= E/t or W/t) = work/time = Fv F = (-) kx E_elas = ½kx²

a = v²/r = 4p²r/T² t = Fr sin Q F_fr = m_kN and F_fr < or = m_sN

F = Gm₁m₂/r² E_p = -Gm₁m₂/r V = -Gm/r T²/R³ = constant

Page 6 Thermal physics and Waves

Q = mcDT Q = mL p = F/A pV = nRT

DQ = DU + DW DW = pDV efficiency = (Q_H - Q_C)/ Q_H

h = Carnot efficiency = (T_H - T_C)/ T_H Q_C/Q_H = T_C/T_H (Carnot cycle)

f = 1/T v = f l f_beat = ½f₁ - f₂ ½

Moving source: f' = f ( 1 / (1 ± v_s/v)) Moving observer: f' = f (1 ± v_o/v)

d sin Q = n l s = lD / d sin Q₁ / sin Q₂ = v₁ / v₂ n = c / v n₁sinQ₁ = n₂sinQ₂

Page 7 : Electricity and magnetism, electromagnetism

F = kq₁q₂/r² where k = 1/4pe₀ E = F / q E = kq / r²

E = - DV / Dx E = V / d V = kq/r where k = 1/4pe₀

I = D q / Dt R = V / I P = VI = I²R = V²/R R = R₁ + R₂

1/R = 1/R₁ + 1/R₂ B = m₀I / 2pr B = m₀NI/L = m₀nI F = ILBsinq

F = qvBsinq F/L = m₀I₁I₂/2pr e = BLv F = BAcosq

e = - NDF/Dt I_rms = I₀ /Ö2 V_rms = V₀/Ö2 V_p/V_s = N_p/N_s

Page 8 : Atomic, nuclear and quantum physics

E = mc² E = hf p = h/l

hf = φ + E_k,max hf = hf₀ + eV_s N = N₀e^-lt T_½=ln 2/l

Page 9-10 : SL options

Page 11 : Biomedical physics and The history and development of physics

b = 10 log ( I / I₀ ) where I₀ = 10^-12 Wm^-2 I = I₀e^-mx x_½ = ln2/m

Mechanical Advantage = load/effort

Velocity Ratio = distance moved by effort/ distance moved by load

Absorbed dose = Absorbed Energy / mass Exposure = total charge / mass

Dose equivalent = quality factor x Absorbed dose

1 / T_E = 1/T_B + 1 / T_R 1 / l = R_H ( 1/n² - 1/m² ) DxDp ³ h/2p DEDt ³ h/2p

Page 12 : Astrophysics and Relativity

L = sAT⁴ l_max = 2.90 x 10^-3 / T d(parsec) = 1 / p(arc-second)

b = L / 4pd² v = Hd Dl / l » v / c

g = 1 / ( 1 - v²/c² )^½ Dt = gDt₀ L = L₀ / g

u_x' = ( u_x - v ) / ( 1 - u_xv/c²)

m = gm₀ p =gm₀u E₀ = m₀c² E = mc²

E² = p²c² + m₀²c⁴ Df / f = gDh / c² R_Sch = 2GM / c²

Page 13 : Optics

n₁sinq₁ = n₂sinq₂ n = 1 / sinq_c 1/f = 1/u + 1/v m = h_i / h_o = v / u

M = q_i / q_o q = l / b q = 1.22l/b d sinq = nl