Some of these formulae should be memorised during your higher level course but the list covers a great deal more than is needed for a simple extension to the foundation course. It is most important that you are sure of the meaning of all the symbols

v = u + at

v

s = ut + ½ at

average vel. = [u + v]/2

Impulse I = Ft

Newton's second law F = d(mv)/dt = ma

Impulse and momentum Ft = mv – mu

Kinetic energy k.e = ½ mv

Potential energy p.e = mgh

Work work = Fs

Power Power = Fv

Pressure (P) = F/A

Pressure at a depth h in a liquid in a liquid (P) = hρg

Density (ρ) = m/V

Couple (C) = Fd

Upthrust (U) = vρg

Maximum height (h) = u

Time of flight t = 2usinA/g

Linear and angular velocity v = rω

Time of rotation period T = 2πr/v = 2π/ω

Centripetal force F = mv

Angular momentum (M) = Iω

Rotational kinetic energy = ½ Iω

Couple (C) = Iα

Work done W = Cθ

Displacement x = rsin(ωt)

Velocity v = ±ω√(r

Acceleration a = -ω

Velocity v = ωr cos (ωt)

Kinetic energy = ½ mω

Potential energy = ½ mω

Total energy E = ½ mω

Newton's law F = Gm

Potential energy p.e = - GmM/r

Kinetic energy k.e = +GmM/2r

Total energy E = - GmM/2r

Potential V

g

g and g

g and g

Escape velocity v = √[2Rg

Strain strain = e/L

Young modulus E = F/LeA

Bulk modulus K = Dp/(Dv/v)

Rigidity or shear modulus (G) G = [F/A]/θ

Potential energy stored = ½ Fe = ½ EAe

Energy per unit volume = ½ stress x strain

Stokes' law F = 6πhrv

Poiseuille's formula Volume s

Excess pressure in air bubble p = 2T/r

Excess pressure in soap bubble p = 4T/r

Related to wave velocities (n) = c

Serial relation n

Thin prism d = (n – 1)A

Critical angle(c) n = 1/sin c

Lens formulae 1/u + 1/v = 1/f

Telescope magnification (m) = f

Angular magnification M = - (D/f+ 1)

Resolving power f = 1.22λ/a

Destructive interference path difference for a minimum= (2m + 1)λ/2

Young's slits ml = x

Newton's rings (dark ring viewed by reflection) mλ = r

Thin film interference mλ = 2nt cos r

Diffraction grating (max) mλ = e sinθ

Brewster's law (polarisation) tan p = n

Malus' law I = I

Travelling wave y = a sin[ωt – kx] = a sin2π[t/T – x/λ]

Standing wave y = 2a cos[2πx/λ]sin[2πt/T]

Velocity of sound (v) = √[γP/ρ]

Frequency of stretched string f

Fundamental frequency (closed tube) f

Intensity of wave I = ka

Beat frequency f = f

Organ pipes:

Open pipe f = (m + 1)f

Closed at one end f = (2m + 1)f

Linear expansivity (α) L

Specific heat capacity (c) H = mcθ

Specific latent heat (L) H = mL

Electrical heating H = VIt

Density change r

Ideal gas equation PV = nRT

Isothermal change PV = constant

Adiabatic change PV

Charles's law V/T = constant

Conduction of heat dH/dt = - kA dθ/dx

Stefan-Boltzmann law E = σA[T

Wien's law λ

First law of thermodynamics dU = dQ + dW

Work done in isothermal change dW = PdV

Kinetic theory equation PV = 1/3 m

Mean square velocity (c

Current I = nAve

Electrical energy = QV

Force on charge F = QE = QV/d

Ohm's law V = IR

Internal resistance E = I[R + r]

Resistivity ρ= RL/A

Temperature variation R

Series resistance R = R

Parallel resistance 1/R = 1/R

Power W = VI = I

Force between point charges F = Q

Field due to point charge Q E = Q/[4εd

Potential V = W/Q

Potential due to charge Q V

Capacitance (C) = Q/V

Capacitance of a sphere (C) = 4πεr

Parallel-plate capacitor C = εA/d

Parallel capacitors C = C

Series capacitors 1/C = 1/C

Energy (E) stored by a capacitor = ½ CV

Capacitor discharge V = V

Capacitor charge V = V

Field at centre of coil of N turns (B) = μ

Field in solenoid (B) = μ

Field at end of long solenoid of N turns (B) = μ

Helmholtz coils field (B) = 8μ

Field near straight wire (B) = μ

Velocity of e.m. waves c = 1/(ε

Mutual inductance M = N

Induced e.m.f. (ε) = -L dI/dt

Induced e.m.f. (ε

Induced e.m.f. in a rotating coil (ε) = BANωsinθ

Induced e.m.f.(Neumann's law) ε = - Ndφ/dt

Transformer n

Root mean square current (I) I = i

Alternating current i = io sin(ωt)

Capacitative reactance X

Inductive reactance X

Impedance (series RLC) Z = [R

Resonance condition for I X

Electromagnetic force on electron F = Bev

Crossed fields eE = Bev

Energy gain E = eV

Kinetic energy eV = ½ mv

Circular orbit Bev = mv

Quantum energy E = hf

Relativistic mass-energy relation E = mc

de Broglie equation λ = h/p = h/mv

Work function W = hf

Einstein's p.e. equation hf = hf

Photoelectric effect hf = eV

A = A

Serial relation λ

Nuclear radius (r) of nucleus of mass number A = r

L = L

t = t

γ = 1/[1-v

m = γm

L = L

t = γt