Equations

Equation index

Every equation used across the notes, grouped by unit and linked back to the lesson it came from. Each is marked according to whether it is printed on the AQA data sheet or is one you have to carry in your head.

The 21 you have to know by heart

These are the ones that do not appear on the data sheet. If you are short of time, learn these first.

Uncertainty and error

percentage uncertainty = uncertaintyvalue × 100

Progressive waves

phase difference = 2πdλ

Interference and Young's double slit

constructive: path difference = nλ

Interference and Young's double slit

destructive: path difference = (n + 12

Constituents of the atom

specific charge = Qm

Potential dividers

Vout = Vin × R2R1 + R2

Orbits and satellites

T2 = 2GM r3

Orbits and satellites

vesc = 2GMr

Nuclear reactors and safety

fraction kept = (M - mM + m)2

Every equation, by unit

Jump to: Measurements · Mechanics · Materials · Waves · Quantum phenomena · Particles · Electricity · Periodic motion · Thermal physics · Gravitational fields · Electric fields · Capacitance · Magnetic fields · Nuclear physics

Measurements1 equation

Uncertainty and error

percentage uncertainty = uncertaintyvalue × 100NOT ON THE DATA SHEET — LEARN IT

Mechanics16 equations

Moments and equilibrium

moment = F dON YOUR DATA SHEET

Motion graphs and the SUVAT equations

v = ΔsΔt     a = ΔvΔtON YOUR DATA SHEET
v = u + atON YOUR DATA SHEET
s = 12(u + v)tON YOUR DATA SHEET
s = ut + 12at2ON YOUR DATA SHEET
v2 = u2 + 2asON YOUR DATA SHEET

Mass and weight

W = mgNOT ON THE DATA SHEET — LEARN IT

Momentum and impulse

p = mvNOT ON THE DATA SHEET — LEARN IT
F = Δ(mv)ΔtON YOUR DATA SHEET
FΔt = Δ(mv)ON YOUR DATA SHEET

Work, energy and power

W = Fscos θON YOUR DATA SHEET
P = ΔWΔt = FvON YOUR DATA SHEET
efficiency = useful output powerinput powerON YOUR DATA SHEET

Conservation of energy

Ek = 12mv2ON YOUR DATA SHEET
ΔEp = mgΔhON YOUR DATA SHEET

Materials6 equations

Density and Hooke's law

ρ = mVON YOUR DATA SHEET
F = kΔLON YOUR DATA SHEET
energy stored = 12FΔLON YOUR DATA SHEET

Stress, strain and the Young modulus

tensile stress = FAON YOUR DATA SHEET
tensile strain = ΔLLON YOUR DATA SHEET
E = tensile stresstensile strain = FLAΔLON YOUR DATA SHEET

Waves13 equations

Progressive waves

f = 1TON YOUR DATA SHEET
c = fλON YOUR DATA SHEET
phase difference = 2πdλNOT ON THE DATA SHEET — LEARN IT

Stationary waves

λn = 2LnNOT ON THE DATA SHEET — LEARN IT
f1 = 12LTμON YOUR DATA SHEET

Refraction and total internal reflection

n = ccsON YOUR DATA SHEET
n1 sin θ1 = n2 sin θ2ON YOUR DATA SHEET
sin θc = n2n1ON YOUR DATA SHEET

Interference and Young's double slit

constructive: path difference = nλNOT ON THE DATA SHEET — LEARN IT
destructive: path difference = (n + 12NOT ON THE DATA SHEET — LEARN IT
w = λDsON YOUR DATA SHEET

Diffraction gratings

d sin θ = nλON YOUR DATA SHEET
d = 1NNOT ON THE DATA SHEET — LEARN IT

Quantum phenomena3 equations

The photoelectric effect

hf = φ + Ek(max)ON YOUR DATA SHEET

Energy levels and photon emission

hf = E1 - E2ON YOUR DATA SHEET

Wave-particle duality

λ = hmvON YOUR DATA SHEET

Particles2 equations

Constituents of the atom

specific charge = QmNOT ON THE DATA SHEET — LEARN IT

Antimatter and photons

E = hf = hcλON YOUR DATA SHEET

Electricity11 equations

Current, charge and the direction problem

I = ΔQΔtON YOUR DATA SHEET
V = WQON YOUR DATA SHEET
R = VION YOUR DATA SHEET

Resistivity and superconductivity

ρ = RALON YOUR DATA SHEET

Circuits and Kirchhoff's laws

RT = R1 + R2 + R3 + …ON YOUR DATA SHEET
1RT = 1R1 + 1R2 + 1R3 + …ON YOUR DATA SHEET
E = IVtNOT ON THE DATA SHEET — LEARN IT
P = IV = I2R = V2RON YOUR DATA SHEET

Potential dividers

Vout = Vin × R2R1 + R2NOT ON THE DATA SHEET — LEARN IT

EMF and internal resistance

ε = EQON YOUR DATA SHEET
ε = I(R + r)ON YOUR DATA SHEET

Periodic motion8 equations

Circular motion

ω = vr = 2πfON YOUR DATA SHEET
a = v2r = ω2rON YOUR DATA SHEET
F = mv2r = mω2rON YOUR DATA SHEET

Simple harmonic motion

a = -ω2xON YOUR DATA SHEET
x = Acos (ωt)ON YOUR DATA SHEET
v = ±ωA2 - x2ON YOUR DATA SHEET

SHM systems: pendulums and springs

T = 2πmkON YOUR DATA SHEET
T = 2πlgON YOUR DATA SHEET

Thermal physics7 equations

Thermal energy transfer and specific heat capacity

Q = mcΔθON YOUR DATA SHEET
Q = mlON YOUR DATA SHEET

Ideal gases and the gas laws

pV = nRTON YOUR DATA SHEET
pV = NkTON YOUR DATA SHEET
W = pΔVNOT ON THE DATA SHEET — LEARN IT

Molecular kinetic theory

pV = 13Nm(crms)2ON YOUR DATA SHEET
12m(crms)2 = 3kT2 = 3RT2NAON YOUR DATA SHEET

Gravitational fields9 equations

Newton's law of gravitation

F = Gm1m2r2ON YOUR DATA SHEET
g = FmON YOUR DATA SHEET
g = GMr2ON YOUR DATA SHEET

Gravitational potential

V = -GMrON YOUR DATA SHEET
ΔW = mΔVON YOUR DATA SHEET
g = -ΔVΔrON YOUR DATA SHEET

Orbits and satellites

GMmr2 = mv2rNOT ON THE DATA SHEET — LEARN IT
T2 = 2GM r3NOT ON THE DATA SHEET — LEARN IT
vesc = 2GMrNOT ON THE DATA SHEET — LEARN IT

Electric fields7 equations

Coulomb's law and electric field strength

F = 14πε0 Q1Q2r2ON YOUR DATA SHEET
E = FQON YOUR DATA SHEET
E = VdON YOUR DATA SHEET
E = 14πε0 Qr2ON YOUR DATA SHEET

Electric potential

V = 14πε0 QrON YOUR DATA SHEET
ΔW = QΔVON YOUR DATA SHEET
E = ΔVΔrON YOUR DATA SHEET

Capacitance6 equations

Capacitors and energy stored

C = QVON YOUR DATA SHEET
C = 0εrdON YOUR DATA SHEET
E = 12QV = 12CV2 = 12Q2CON YOUR DATA SHEET

The time constant and exponential decay

T½ = 0.69RCNOT ON THE DATA SHEET — LEARN IT
Q = Q0e-t/RCON YOUR DATA SHEET
Q = Q0(1 - e-t/RC)ON YOUR DATA SHEET

Magnetic fields11 equations

Force on a moving charge

F = BQvON YOUR DATA SHEET
r = mvBQNOT ON THE DATA SHEET — LEARN IT

Magnetic flux and flux linkage

Φ = BAON YOUR DATA SHEET
NΦ = BANcos θON YOUR DATA SHEET

Electromagnetic induction: Faraday and Lenz

ε = NΔΦΔtON YOUR DATA SHEET
ε = BANωsin ω tON YOUR DATA SHEET

Alternating currents

Irms = I02ON YOUR DATA SHEET
Vrms = V02ON YOUR DATA SHEET

Transformers

NsNp = VsVpON YOUR DATA SHEET
efficiency = IsVsIpVpON YOUR DATA SHEET

Nuclear physics11 equations

Radioactive decay and half-life

ΔNΔt = -λNON YOUR DATA SHEET
A = λNON YOUR DATA SHEET
N = N0e-λtON YOUR DATA SHEET
T½ = ln 2λON YOUR DATA SHEET
A = A0e-λtNOT ON THE DATA SHEET — LEARN IT

Nuclear radius and density

Ek = Qq4πε0rminNOT ON THE DATA SHEET — LEARN IT
R = R0A1/3ON YOUR DATA SHEET
ρ = 3u4πR03NOT ON THE DATA SHEET — LEARN IT

Mass-energy and binding energy

E = mc2ON YOUR DATA SHEET

Nuclear reactors and safety

fraction kept = (M - mM + m)2NOT ON THE DATA SHEET — LEARN IT

111 equations in total, 21 of them off the data sheet. See also key ideas, command words and the revision checklist.