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
Mass and weight
W = mg
Momentum and impulse
p = mv
Progressive waves
phase difference = 2πdλ
Stationary waves
λn = 2Ln
Interference and Young's double slit
constructive: path difference = nλ
Interference and Young's double slit
destructive: path difference = (n + 12)λ
Diffraction gratings
d = 1N
Constituents of the atom
specific charge = Qm
Potential dividers
Vout = Vin × R2R1 + R2
Ideal gases and the gas laws
W = pΔV
Orbits and satellites
GMmr2 = mv2r
Orbits and satellites
T2 = 4π2GM r3
Orbits and satellites
vesc = √2GMr
The time constant and exponential decay
T½ = 0.69RC
Force on a moving charge
r = mvBQ
Radioactive decay and half-life
A = A0e-λt
Nuclear radius and density
Ek = Qq4πε0rmin
Nuclear radius and density
ρ = 3u4πR03
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
Newton's laws and the resultant force
F = maON 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
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
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 + 12)λNOT ON THE DATA SHEET — LEARN IT
w = λDsON YOUR DATA SHEET
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
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 = ±ω√A2 - x2ON 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 = 4π2GM 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 = Aε0εrdON 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
Magnetic flux density and the force on a wire
F = BIlON YOUR DATA SHEET
Electromagnetic induction: Faraday and Lenz
ε = NΔΦΔtON YOUR DATA SHEET
ε = BANωsin ω tON YOUR DATA SHEET
Nuclear physics11 equations
Rutherford scattering and the nuclear atom
I = kx2ON YOUR DATA SHEET
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.