Equations

Equation sheet, and the ones to memorise

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.

213 equations

The 22 to 25 you have to know by heartNot on the AQA data sheet: 21 core, plus your one option34 equations

21 of these are core, and everybody sits them. The other 13 sit in the five option units, of which you take exactly one: Electronics 4, Medical physics 4, Astrophysics 3, Engineering physics 1, Turning points 1. So the number you personally have to carry is 22 to 25. 34 is the size of this catalogue, not the size of anybody’s revision list.

Uncertainty and error

percentage uncertainty=uncertaintyvalue×100\text{percentage uncertainty} = \frac{\text{uncertainty}}{\text{value}} \times 100

Mass and weight

W=mgW = mg

Momentum and impulse

p=mvp = mv

Progressive waves

phase difference=2πdλ\text{phase difference} = \frac{2\pi d}{\lambda}

Stationary waves

λn=2Ln\lambda_n = \frac{2L}{n}

Interference and Young's double slit

constructive: path difference=nλ\text{constructive: path difference} = n\lambda

Interference and Young's double slit

destructive: path difference=(n+12)λ\text{destructive: path difference} = (n + \tfrac{1}{2})\lambda

Diffraction gratings

d=1Nd = \frac{1}{N}

Constituents of the atom

specific charge=Qm\text{specific charge} = \frac{Q}{m}

Circuits and Kirchhoff's laws

E=IVtE = IVt

Potential dividers

Vout=Vin×R2R1+R2V_{out} = V_{in} \times \frac{R_{2}}{R_{1} + R_{2}}

Unloaded divider: the output must draw negligible current.

Ideal gases and the gas laws

W=pΔVW = p\Delta V

Constant pressure; W is the work done by the gas.

Orbits and satellites

GMmr2=mv2r\frac{GMm}{r^{2}} = \frac{mv^{2}}{r}

Orbits and satellites

T2=4π2GMr3T^{2} = \frac{4\pi^{2}}{GM}\,r^{3}

Orbits and satellites

vesc=2GMrv_{esc} = \sqrt{\frac{2GM}{r}}

The time constant and exponential decay

T½=0.69RCT_{½} = 0.69RC

Force on a moving charge

r=mvBQr = \frac{mv}{BQ}

v perpendicular to B; non-relativistic, so p = mv.

Radioactive decay and half-life

A=A0e-λtA = A_{0}e^{-λt}

Nuclear radius and density

Ek=Qq4πε0rminE_{k} = \frac{Qq}{4πε_{0}r_{min}}

Nuclear radius and density

ρ=3u4πR03ρ = \frac{3u}{4πR_{0}^{3}}

Nuclear reactors and safety

fraction kept=(M-mM+m)2\text{fraction kept} = (\frac{M - m}{M + m})^{2}

Discrete semiconductor devices · option

I=VS-VZRSI = \frac{V_{S} - V_{Z}}{R_{S}}

Resonant circuits and filters · option

fc=12πRCf_{c} = \frac{1}{2\pi RC}

Operational amplifiers · option

gain×bandwidth=constant\text{gain} \times \text{bandwidth} = \text{constant}

Digital signal processing · option

fout=fin2nf_{out} = \frac{f_{in}}{2^{n}}

Rotational motion and moment of inertia · option

a=αra = \alpha r

Telescopes across the spectrum · option

collecting power∝D2\text{collecting power} \propto D^{2}

Star brightness and magnitude · option

F=L4πd2F = \frac{L}{4\pi d^{2}}

The Doppler effect and Hubble's law · option

fo=fsvv-vsf_{o} = \frac{f_{s}v}{v - v_{s}}

The consequences of special relativity · option

Ek=(m−m0)c2E_{k} = (m − m_{0})c^{2}

Ultrasound imaging · option

d=ct2d = \frac{ct}{2}

X-rays and CT scanning · option

Emax=eVE_{max} = eV

The physics of the ear · option

I=PAI = \frac{P}{A}

The physics of the ear · option

relative intensity level=10logI2I1\text{relative intensity level} = 10\,\text{log}\frac{I_{2}}{I_{1}}
MeasurementsYear 121 equations

Uncertainty and error

percentage uncertainty=uncertaintyvalue×100\text{percentage uncertainty} = \frac{\text{uncertainty}}{\text{value}} \times 100NOT ON THE AQA DATA SHEET: LEARN IT
MechanicsYear 1217 equations

Moments and equilibrium

moment=Fd\text{moment} = F dON THE AQA DATA SHEET

Motion graphs and the SUVAT equations

v=ΔsΔta=ΔvΔtv = \frac{\Delta s}{\Delta t} \qquad a = \frac{\Delta v}{\Delta t}ON THE AQA DATA SHEET
v=u+atv = u + atON THE AQA DATA SHEET
s=12(u+v)ts = \tfrac{1}{2}(u + v)tON THE AQA DATA SHEET
s=ut+12at2s = ut + \tfrac{1}{2}at^{2}ON THE AQA DATA SHEET
v2=u2+2asv^{2} = u^{2} + 2asON THE AQA DATA SHEET

Newton's laws and the resultant force

F=maF = maON THE AQA DATA SHEET

Mass and weight

W=mgW = mgNOT ON THE AQA DATA SHEET: LEARN IT

Momentum and impulse

p=mvp = mvNOT ON THE AQA DATA SHEET: LEARN IT
F=Δ(mv)ΔtF = \frac{\Delta(mv)}{\Delta t}ON THE AQA DATA SHEET
Ek=p22mE_{k} = \frac{p^{2}}{2m}
FΔt=Δ(mv)F\Delta t = \Delta(mv)ON THE AQA DATA SHEET

Work, energy and power

W=FscosθW = Fs\cos\thetaON THE AQA DATA SHEET
P=ΔWΔt=FvP = \frac{\Delta W}{\Delta t} = FvON THE AQA DATA SHEET
efficiency=useful output powerinput power\text{efficiency} = \frac{\text{useful output power}}{\text{input power}}ON THE AQA DATA SHEET

Conservation of energy

Ek=12mv2E_{k} = \tfrac{1}{2}mv^{2}ON THE AQA DATA SHEET
ΔEp=mgΔh\Delta E_{p} = mg\Delta hON THE AQA DATA SHEET
MaterialsYear 1210 equations

Density and Hooke's law

ρ=mV\rho = \frac{m}{V}ON THE AQA DATA SHEET
F=kΔLF = k\Delta LON THE AQA DATA SHEET
energy stored=12FΔL\text{energy stored} = \tfrac{1}{2}F\Delta LON THE AQA DATA SHEET

Stress, strain and the Young modulus

tensile stress=FA\text{tensile stress} = \frac{F}{A}ON THE AQA DATA SHEET
tensile strain=ΔLL\text{tensile strain} = \frac{\Delta L}{L}ON THE AQA DATA SHEET
E=tensile stresstensile strainE = \frac{\text{tensile stress}}{\text{tensile strain}}ON THE AQA DATA SHEET

Fluids: pressure, upthrust and viscosity

p=FAp = \frac{F}{A}
Δp=ρAgΔhA=ρgΔh\Delta p = \frac{\rho A g \Delta h}{A} = \rho g \Delta h
p=ρghp = \rho g h
F=6πηrvF = 6\pi\eta r v
WavesYear 1222 equations

Progressive waves

f=1Tf = \frac{1}{T}ON THE AQA DATA SHEET
c=fλc = f\lambdaON THE AQA DATA SHEET
phase difference=2πdλ\text{phase difference} = \frac{2\pi d}{\lambda}NOT ON THE AQA DATA SHEET: LEARN IT

Longitudinal, transverse and polarisation

I=I0cos2θI = I_0\cos^2\theta

Stationary waves

λn=2Ln\lambda_n = \frac{2L}{n}NOT ON THE AQA DATA SHEET: LEARN IT
v=Tμv = \sqrt{\frac{T}{\mu}}
f1=12LTμf_1 = \frac{1}{2L}\sqrt{\frac{T}{\mu}}ON THE AQA DATA SHEET
λ1=4L\lambda_1 = 4L

Closed pipe, ideal length: one end closed, end corrections neglected.

λn=4Ln\lambda_n = \frac{4L}{n}

Closed pipe: odd harmonics only, n = 1, 3, 5, …

v=2f(L2-L1)v = 2f(L_2 - L_1)

Refraction and total internal reflection

n=ccsn = \frac{c}{c_s}ON THE AQA DATA SHEET
n1sinθ1=n2sinθ2n_1 \sin\theta_1 = n_2 \sin\theta_2ON THE AQA DATA SHEET
n=sinθ1sinθ2n = \frac{\sin\theta_1}{\sin\theta_2}
sinθc=n2n1\sin\theta_c = \frac{n_2}{n_1}ON THE AQA DATA SHEET

Interference and Young's double slit

constructive: path difference=nλ\text{constructive: path difference} = n\lambdaNOT ON THE AQA DATA SHEET: LEARN IT
destructive: path difference=(n+12)λ\text{destructive: path difference} = (n + \tfrac{1}{2})\lambdaNOT ON THE AQA DATA SHEET: LEARN IT
w=λDsw = \frac{\lambda D}{s}ON THE AQA DATA SHEET

Diffraction gratings

dsinθ=nλd \sin\theta = n\lambdaON THE AQA DATA SHEET
d=1Nd = \frac{1}{N}NOT ON THE AQA DATA SHEET: LEARN IT

Lenses and images

P=1fP = \frac{1}{f}
1u+1v=1f\frac{1}{u} + \frac{1}{v} = \frac{1}{f}
m=vum = \frac{v}{u}
Quantum phenomenaYear 123 equations

The photoelectric effect

hf=φ+Ek(max)hf = \phi + E_{k}(max)ON THE AQA DATA SHEET

Energy levels and photon emission

hf=E1-E2hf = E_{1} - E_{2}ON THE AQA DATA SHEET

Wave-particle duality

λ=hmv\lambda = \frac{h}{mv}ON THE AQA DATA SHEET
ParticlesYear 122 equations

Constituents of the atom

specific charge=Qm\text{specific charge} = \frac{Q}{m}NOT ON THE AQA DATA SHEET: LEARN IT

Antimatter and photons

E=hf=hcλE = hf = \frac{hc}{\lambda}ON THE AQA DATA SHEET
ElectricityYear 1214 equations

Current, charge and the direction problem

I=ΔQΔtI = \frac{\Delta Q}{\Delta t}ON THE AQA DATA SHEET
V=WQV = \frac{W}{Q}ON THE AQA DATA SHEET
I=nAvqI = nAvq
R=VIR = \frac{V}{I}ON THE AQA DATA SHEET

Resistivity and superconductivity

ρ=RAL\rho = \frac{RA}{L}ON THE AQA DATA SHEET

Circuits and Kirchhoff's laws

RT=R1+R2+R3+…R_{T} = R_{1} + R_{2} + R_{3} + \ldotsON THE AQA DATA SHEET
1RT=1R1+1R2+1R3+…\frac{1}{R_{T}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \ldotsON THE AQA DATA SHEET
E=IVtE = IVtNOT ON THE AQA DATA SHEET: LEARN IT
P=IV=I2R=V2RP = IV = I^{2}R = \frac{V^{2}}{R}ON THE AQA DATA SHEET

Potential dividers

Vout=Vin×R2R1+R2V_{out} = V_{in} \times \frac{R_{2}}{R_{1} + R_{2}}NOT ON THE AQA DATA SHEET: LEARN IT

Unloaded divider: the output must draw negligible current.

Vx=VxLV_{x} = V\frac{x}{L}
E1E2=l1l2\frac{E_{1}}{E_{2}} = \frac{l_{1}}{l_{2}}

EMF and internal resistance

ε=EQ\epsilon = \frac{E}{Q}ON THE AQA DATA SHEET
ε=I(R+r)\epsilon = I(R + r)ON THE AQA DATA SHEET
Periodic motionYear 1311 equations

Circular motion

ω=vr=2πf\omega = \frac{v}{r} = 2\pi fON THE AQA DATA SHEET
a=ΔvΔt=vΔθΔθ/ω=vωa = \frac{\Delta v}{\Delta t} = \frac{v\Delta\theta}{\Delta\theta/\omega} = v\omega
a=v2r=ω2ra = \frac{v^{2}}{r} = \omega^{2}rON THE AQA DATA SHEET
F=mv2r=mω2rF = \frac{mv^{2}}{r} = m\omega^{2}rON THE AQA DATA SHEET

Simple harmonic motion

a=-ω2xa = -\omega^{2}xON THE AQA DATA SHEET
x=Acos(ωt)x = A\cos(\omega t)ON THE AQA DATA SHEET
v=±ωA2-x2v = \pm\omega\sqrt{A^{2} - x^{2}}ON THE AQA DATA SHEET

SHM systems: pendulums and springs

T=2πmkT = 2\pi\sqrt{\frac{m}{k}}ON THE AQA DATA SHEET
T=2πlgT = 2\pi\sqrt{\frac{l}{g}}ON THE AQA DATA SHEET
E=12kA2E = \frac{1}{2}kA^{2}
E=12mω2x02E = \frac{1}{2}m\omega^{2}x_{0}^{2}
Thermal physicsYear 138 equations

Thermal energy transfer and specific heat capacity

Q=mcΔθQ = mc\Delta\thetaON THE AQA DATA SHEET
P1−P2=(m1−m2)cΔθP_{1} − P_{2} = (m_{1} − m_{2})c\Delta\theta
Q=mlQ = mlON THE AQA DATA SHEET

Ideal gases and the gas laws

pV=nRTpV = nRTON THE AQA DATA SHEET
pV=NkTpV = NkTON THE AQA DATA SHEET
W=pΔVW = p\Delta VNOT ON THE AQA DATA SHEET: LEARN IT

Constant pressure; W is the work done by the gas.

Molecular kinetic theory

pV=13Nm(crms)2pV = \frac{1}{3}Nm(c_{rms})^{2}ON THE AQA DATA SHEET
12m(crms)2=3kT2=3RT2NA\frac{1}{2}m(c_{rms})^{2} = \frac{3kT}{2} = \frac{3RT}{2N_{A}}ON THE AQA DATA SHEET
Gravitational fieldsYear 139 equations

Newton's law of gravitation

F=Gm1m2r2F = \frac{Gm_{1}m_{2}}{r^{2}}ON THE AQA DATA SHEET
g=Fmg = \frac{F}{m}ON THE AQA DATA SHEET
g=GMr2g = \frac{GM}{r^{2}}ON THE AQA DATA SHEET

Gravitational potential

V=-GMrV = -\frac{GM}{r}ON THE AQA DATA SHEET
ΔW=mΔV\Delta W = m\Delta VON THE AQA DATA SHEET
g=-ΔVΔrg = -\frac{\Delta V}{\Delta r}ON THE AQA DATA SHEET

Orbits and satellites

GMmr2=mv2r\frac{GMm}{r^{2}} = \frac{mv^{2}}{r}NOT ON THE AQA DATA SHEET: LEARN IT
T2=4π2GMr3T^{2} = \frac{4\pi^{2}}{GM}\,r^{3}NOT ON THE AQA DATA SHEET: LEARN IT
vesc=2GMrv_{esc} = \sqrt{\frac{2GM}{r}}NOT ON THE AQA DATA SHEET: LEARN IT
Electric fieldsYear 137 equations

Coulomb's law and electric field strength

F=14πε0Q1Q2r2F = \frac{1}{4\piε_{0}}\,\frac{Q_{1}Q_{2}}{r^{2}}ON THE AQA DATA SHEET
E=FQE = \frac{F}{Q}ON THE AQA DATA SHEET
E=VdE = \frac{V}{d}ON THE AQA DATA SHEET
E=14πε0Qr2E = \frac{1}{4\piε_{0}}\,\frac{Q}{r^{2}}ON THE AQA DATA SHEET

Electric potential

V=14πε0QrV = \frac{1}{4\piε_{0}}\,\frac{Q}{r}ON THE AQA DATA SHEET
ΔW=QΔV\Delta W = Q\Delta VON THE AQA DATA SHEET
E=ΔVΔrE = \frac{\Delta V}{\Delta r}ON THE AQA DATA SHEET
CapacitanceYear 139 equations

Capacitors and energy stored

C=QVC = \frac{Q}{V}ON THE AQA DATA SHEET
C=4πε0rC = 4\piε_{0}r
C=Aε0εrdC = \frac{Aε_{0}ε_{r}}{d}ON THE AQA DATA SHEET
E=12QV=12CV2=12Q2CE = \frac{1}{2}QV = \frac{1}{2}CV^{2} = \frac{1}{2}\frac{Q^{2}}{C}ON THE AQA DATA SHEET
C=C1+C2+…C = C_{1} + C_{2} + \ldots
1C=1C1+1C2+…\frac{1}{C} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \ldots

The time constant and exponential decay

T½=0.69RCT_{½} = 0.69RCNOT ON THE AQA DATA SHEET: LEARN IT
Q=Q0e-t/RCQ = Q_{0}e^{-t/RC}ON THE AQA DATA SHEET
Q=Q0(1-e-t/RC)Q = Q_{0}(1 - e^{-t/RC})ON THE AQA DATA SHEET
Magnetic fieldsYear 1314 equations

Magnetic flux density and the force on a wire

F=BIlF = BIlON THE AQA DATA SHEET
F=BIlsinθF = BIl \sin\theta

Force on a moving charge

F=BQvF = BQvON THE AQA DATA SHEET
F=BQvsinθF = BQv \sin\theta
r=mvBQr = \frac{mv}{BQ}NOT ON THE AQA DATA SHEET: LEARN IT

v perpendicular to B; non-relativistic, so p = mv.

VH=BIntqV_{H} = \frac{BI}{ntq}

Magnetic flux and flux linkage

Φ=BAΦ = BAON THE AQA DATA SHEET

B uniform and along the normal to the area A.

NΦ=BANcosθNΦ = BAN\cosθON THE AQA DATA SHEET

Electromagnetic induction: Faraday and Lenz

ε=NΔΦΔtε = N\frac{\DeltaΦ}{\Delta t}ON THE AQA DATA SHEET
ε=BANωsinωtε = BANω\sinω tON THE AQA DATA SHEET

Alternating currents

Irms=I02I_{rms} = \frac{I_{0}}{\sqrt{2}}ON THE AQA DATA SHEET
Vrms=V02V_{rms} = \frac{V_{0}}{\sqrt{2}}ON THE AQA DATA SHEET

Transformers

NsNp=VsVp\frac{N_{s}}{N_{p}} = \frac{V_{s}}{V_{p}}ON THE AQA DATA SHEET
efficiency=IsVsIpVp\mathrm{efficiency} = \frac{I_{s}V_{s}}{I_{p}V_{p}}ON THE AQA DATA SHEET
Nuclear physicsYear 1311 equations

Rutherford scattering and the nuclear atom

I=kx2I = \frac{k}{x^{2}}ON THE AQA DATA SHEET

Radioactive decay and half-life

ΔNΔt=-λN\frac{\Delta N}{\Delta t} = -λNON THE AQA DATA SHEET
A=λNA = λNON THE AQA DATA SHEET
N=N0e-λtN = N_{0}e^{-λt}ON THE AQA DATA SHEET
T½=ln2λT_{½} = \frac{\text{ln}\,2}{λ}ON THE AQA DATA SHEET
A=A0e-λtA = A_{0}e^{-λt}NOT ON THE AQA DATA SHEET: LEARN IT

Nuclear radius and density

Ek=Qq4πε0rminE_{k} = \frac{Qq}{4πε_{0}r_{min}}NOT ON THE AQA DATA SHEET: LEARN IT
R=R0A1/3R = R_{0}A^{1/3}ON THE AQA DATA SHEET
ρ=3u4πR03ρ = \frac{3u}{4πR_{0}^{3}}NOT ON THE AQA DATA SHEET: LEARN IT

Mass-energy and binding energy

E=mc2E = mc^{2}ON THE AQA DATA SHEET

Nuclear reactors and safety

fraction kept=(M-mM+m)2\text{fraction kept} = (\frac{M - m}{M + m})^{2}NOT ON THE AQA DATA SHEET: LEARN IT
ElectronicsYear 1313 equations

Discrete semiconductor devices

I=VS-VZRSI = \frac{V_{S} - V_{Z}}{R_{S}}NOT ON THE AQA DATA SHEET: LEARN IT

Resonant circuits and filters

f0=12πLCf_{0} = \frac{1}{2\pi\sqrt{LC}}ON THE AQA DATA SHEET
Q=f0fBQ = \frac{f_{0}}{f_{B}}ON THE AQA DATA SHEET
fc=12πRCf_{c} = \frac{1}{2\pi RC}NOT ON THE AQA DATA SHEET: LEARN IT

Operational amplifiers

Vout=AOL(V+-V-)V_{out} = A_{OL}(V_{+} - V_{-})ON THE AQA DATA SHEET
VoutVin=-RfRin\frac{V_{out}}{V_{in}} = -\frac{R_{f}}{R_{in}}ON THE AQA DATA SHEET
VoutVin=1+RfR1\frac{V_{out}}{V_{in}} = 1 + \frac{R_{f}}{R_{1}}ON THE AQA DATA SHEET
gain×bandwidth=constant\text{gain} \times \text{bandwidth} = \text{constant}NOT ON THE AQA DATA SHEET: LEARN IT

Summing and difference amplifiers

Vout=-Rf(V1R1+V2R2+V3R3+...)V_{out} = -R_{f}(\frac{V_{1}}{R_{1}} + \frac{V_{2}}{R_{2}} + \frac{V_{3}}{R_{3}} + ...)ON THE AQA DATA SHEET
Vout=(V+-V-)RfR1V_{out} = (V_{+} - V_{-})\frac{R_{f}}{R_{1}}ON THE AQA DATA SHEET

Digital signal processing

fout=fin2nf_{out} = \frac{f_{in}}{2^{n}}NOT ON THE AQA DATA SHEET: LEARN IT

Data communication

AM bandwidth=2fM\text{AM bandwidth} = 2f_{M}ON THE AQA DATA SHEET
FM bandwidth=2(Δf+fM)\text{FM bandwidth} = 2(\Delta f + f_{M})ON THE AQA DATA SHEET
Engineering physicsYear 1325 equations

Rotational motion and moment of inertia

a=αra = \alpha rNOT ON THE AQA DATA SHEET: LEARN IT
ω2=ω1+αt\omega_{2} = \omega_{1} + \alpha tON THE AQA DATA SHEET
ω22=ω12+2αθ\omega_{2}^{2} = \omega_{1}^{2} + 2\alpha\thetaON THE AQA DATA SHEET
θ=ω1t+αt22\theta = \omega_{1}t + \frac{\alpha t^{2}}{2}ON THE AQA DATA SHEET
θ=(ω1+ω2)t2\theta = \frac{(\omega_{1} + \omega_{2})t}{2}ON THE AQA DATA SHEET
I=m1r12+m2r22+…I = m_{1}r_{1}^{2} + m_{2}r_{2}^{2} + \ldotsON THE AQA DATA SHEET
Ek=12Iω2E_{k} = \frac{1}{2}I\omega^{2}ON THE AQA DATA SHEET

Torque, angular momentum and rotational power

T=FrT = FrON THE AQA DATA SHEET
T=IαT = I\alphaON THE AQA DATA SHEET
angular momentum=Iω\text{angular momentum} = I\omegaON THE AQA DATA SHEET
TΔt=Δ(Iω)T\Delta t = \Delta(I\omega)ON THE AQA DATA SHEET
W=TθW = T\thetaON THE AQA DATA SHEET
P=TωP = T\omegaON THE AQA DATA SHEET

The first law of thermodynamics

Q=ΔU+WQ = \Delta U + WON THE AQA DATA SHEET
W=pΔVW = p\Delta VON THE AQA DATA SHEET

Constant pressure; W is the work done by the gas.

pV=constantpV = \text{constant}ON THE AQA DATA SHEET
pVγ=constantpV^{\gamma} = \text{constant}ON THE AQA DATA SHEET

Heat engines and heat pumps

efficiency=WQH=QH−QCQH\text{efficiency} = \frac{W}{Q_{H}} = \frac{Q_{H} − Q_{C}}{Q_{H}}ON THE AQA DATA SHEET
maximum theoretical efficiency=TH−TCTH\text{maximum theoretical efficiency} = \frac{T_{H} − T_{C}}{T_{H}}ON THE AQA DATA SHEET
input power=calorific value×fuel flow rate\text{input power} = \text{calorific value} \times \text{fuel flow rate}ON THE AQA DATA SHEET
indicated power=area of loop×cycles per second×cylinders\text{indicated power} = \text{area of loop} \times \text{cycles per second} \times \text{cylinders}ON THE AQA DATA SHEET
P=TωP = T\omegaON THE AQA DATA SHEET
friction power=indicated power−brake power\text{friction power} = \text{indicated power} − \text{brake power}ON THE AQA DATA SHEET
COPref=QCW=QCQH−QCCOP_{ref} = \frac{Q_{C}}{W} = \frac{Q_{C}}{Q_{H} − Q_{C}}ON THE AQA DATA SHEET
COPhp=QHW=QHQH−QCCOP_{hp} = \frac{Q_{H}}{W} = \frac{Q_{H}}{Q_{H} − Q_{C}}ON THE AQA DATA SHEET
AstrophysicsYear 1313 equations

Telescopes and image formation

M=fofeM = \frac{f_{o}}{f_{e}}ON THE AQA DATA SHEET

Telescopes across the spectrum

θ≈λD\theta \approx \frac{\lambda}{D}ON THE AQA DATA SHEET
collecting power∝D2\text{collecting power} \propto D^{2}NOT ON THE AQA DATA SHEET: LEARN IT

Star brightness and magnitude

F=L4πd2F = \frac{L}{4\pi d^{2}}NOT ON THE AQA DATA SHEET: LEARN IT
p=1dp = \frac{1}{d}
m−M=5logd10m − M = 5\,\text{log}\frac{d}{10}ON THE AQA DATA SHEET

Black-body radiation and spectral classes

P=σAT4P = \sigma A T^{4}ON THE AQA DATA SHEET
λmaxT=2.9×10−3m K\lambda_{max} T = 2.9 × 10^{−3}\,\text{m K}ON THE AQA DATA SHEET

The HR diagram and stellar evolution

Rs≈2GMc2R_{s} ≈ \frac{2GM}{c^{2}}ON THE AQA DATA SHEET

The Doppler effect and Hubble's law

fo=fsvv-vsf_{o} = \frac{f_{s}v}{v - v_{s}}NOT ON THE AQA DATA SHEET: LEARN IT
Δff=vc\frac{\Delta f}{f} = \frac{v}{c}ON THE AQA DATA SHEET

Approximation for v much less than c.

z=Δλλz = \frac{\Delta \lambda}{\lambda}ON THE AQA DATA SHEET
v=Hdv = HdON THE AQA DATA SHEET
Turning pointsYear 1310 equations

Cathode rays and the electron

eV=12mv2eV = \frac{1}{2}mv^{2}ON THE AQA DATA SHEET

Millikan's oil drop experiment

QVd=mg\frac{QV}{d} = mgON THE AQA DATA SHEET
F=6πηrvF = 6\pi \eta rvON THE AQA DATA SHEET

The nature of light

c=1μ0ε0c = \frac{1}{\sqrt{\mu_{0}\epsilon_{0}}}ON THE AQA DATA SHEET

Quanta and wave-particle duality

p=hλp = \frac{h}{\lambda}ON THE AQA DATA SHEET
λ=h2meV\lambda = \frac{h}{\sqrt{2meV}}ON THE AQA DATA SHEET

The consequences of special relativity

t=t01−v2/c2t = \frac{t_{0}}{\sqrt{1 − v^{2}/c^{2}}}ON THE AQA DATA SHEET
l=l01−v2/c2l = l_{0}\sqrt{1 − v^{2}/c^{2}}ON THE AQA DATA SHEET
E=mc2=m0c21−v2/c2E = mc^{2} = \frac{m_{0}c^{2}}{\sqrt{1 − v^{2}/c^{2}}}ON THE AQA DATA SHEET
Ek=(m−m0)c2E_{k} = (m − m_{0})c^{2}NOT ON THE AQA DATA SHEET: LEARN IT
Medical physicsYear 1314 equations

Ultrasound imaging

d=ct2d = \frac{ct}{2}NOT ON THE AQA DATA SHEET: LEARN IT
Z=ρcZ = \rho cON THE AQA DATA SHEET
IrI0=(Z2-Z1)2(Z2+Z1)2\frac{I_{r}}{I_{0}} = \frac{(Z_{2} - Z_{1})^{2}}{(Z_{2} + Z_{1})^{2}}ON THE AQA DATA SHEET
I=I0e-μxI = I_{0}e^{-\mu x}
Δff=2vcosθc\frac{\Delta f}{f} = \frac{2v\,\cos\theta}{c}

X-rays and CT scanning

Emax=eVE_{max} = eVNOT ON THE AQA DATA SHEET: LEARN IT
I=I0e-μxI = I_{0}e^{-\mu x}ON THE AQA DATA SHEET
μm=μρ\mu_{m} = \frac{\mu}{\rho}ON THE AQA DATA SHEET

The physics of the eye

P=1fP = \frac{1}{f}ON THE AQA DATA SHEET
1u+1v=1f\frac{1}{u} + \frac{1}{v} = \frac{1}{f}ON THE AQA DATA SHEET
m=vum = \frac{v}{u}ON THE AQA DATA SHEET

The physics of the ear

I=PAI = \frac{P}{A}NOT ON THE AQA DATA SHEET: LEARN IT
intensity level=10logII0\text{intensity level} = 10\,\text{log}\frac{I}{I_{0}}ON THE AQA DATA SHEET
relative intensity level=10logI2I1\text{relative intensity level} = 10\,\text{log}\frac{I_{2}}{I_{1}}NOT ON THE AQA DATA SHEET: LEARN IT

213 equations in total. 34 of them are off the AQA data sheet across every option together, which is 22 to 25 for any one student. See also key ideas, command words and the revision checklist.