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Physics Equations - A-Levels Physics

Students need not memorise formulae for this qualification.

The formulae below will be supplied in each examination. Any other formulae that are required will be provided in the question. Symbols used comply with the Association for Science Education (ASE) guidelines (which are based on International Union of Pure and Applied Physics (IUPAP) recommendations).

Mechanics Expected Formulas

Kinematic equations of motion

Displacement with average velocity
s=(u+v)t2\boldsymbol{s = \frac{(u + v)t}{2}}
Velocity-time relation
v=u+at\boldsymbol{v = u + at}
Displacement-time relation
s=ut+12at2\boldsymbol{s = ut + \frac{1}{2}at^2}
Velocity-displacement relation
v2=u2+2as\boldsymbol{v^2 = u^2 + 2as}

Forces

Newton's second law
∑F=ma\boldsymbol{\sum F = ma}
Gravitational field strength
g=Fm\boldsymbol{g = \frac{F}{m}}
Weight
W=mg\boldsymbol{W = mg}
Moment of force
Moment of force=Fx\boldsymbol{\text{Moment of force} = Fx}

Momentum

Linear momentum
p=mv\boldsymbol{p = mv}

Work, energy and power

Work done
ΔW=FΔs\boldsymbol{\Delta W = F\Delta s}
Kinetic energy
Ek=12mv2\boldsymbol{E_k = \frac{1}{2}mv^2}
Gravitational potential energy
ΔEgrav=mgΔh\boldsymbol{\Delta E_{\text{grav}} = mg\Delta h}
Power from energy
P=Et\boldsymbol{P = \frac{E}{t}}
Power from work
P=Wt\boldsymbol{P = \frac{W}{t}}
Energy efficiency
efficiency=useful energy outputtotal energy input\boldsymbol{\text{efficiency} = \frac{\text{useful energy output}}{\text{total energy input}}}
Power efficiency
efficiency=useful power outputtotal power input\boldsymbol{\text{efficiency} = \frac{\text{useful power output}}{\text{total power input}}}

Electricity Expected Formulas

Electricity Equations

Potential difference
V=WQ\boldsymbol{V = \frac{W}{Q}}
Resistance
R=VI\boldsymbol{R = \frac{V}{I}}
Electrical power (current-voltage)
P=VI\boldsymbol{P = VI}
Electrical power (current-resistance)
P=I2R\boldsymbol{P = I^2 R}
Electrical power (voltage-resistance)
P=V2R\boldsymbol{P = \frac{V^2}{R}}
Electrical energy
W=VIt\boldsymbol{W = VIt}
Resistivity
R=ρlA\boldsymbol{R = \frac{\rho l}{A}}
Current from charge flow
I=ΔQΔt\boldsymbol{I = \frac{\Delta Q}{\Delta t}}
Current from drift velocity
I=nqvA\boldsymbol{I = nqvA}

Materials Expected Formulas

Materials Equations

Density
ρ=mV\boldsymbol{\rho = \frac{m}{V}}
Stokes' law
F=6πηrv\boldsymbol{F = 6\pi\eta rv}
Hooke's law
F=kΔx\boldsymbol{F = k\Delta x}
Pressure
p=FA\boldsymbol{p = \frac{F}{A}}
Tensile or compressive stress
Stress σ=FA\boldsymbol{\text{Stress } \sigma = \frac{F}{A}}
Tensile or compressive strain
Strain ε=Δxx\boldsymbol{\text{Strain } \varepsilon = \frac{\Delta x}{x}}
Young modulus
E=σε\boldsymbol{E = \frac{\sigma}{\varepsilon}}
Elastic strain energy
ΔEel=12FΔx\boldsymbol{\Delta E_{\text{el}} = \frac{1}{2}F\Delta x}

Waves and Particle Nature of Light Expected Formulas

Waves and Light Equations

Wave speed
v=fλ\boldsymbol{v = f\lambda}
Speed of a transverse wave on a string
v=Tμ\boldsymbol{v = \sqrt{\frac{T}{\mu}}}
Intensity of radiation
I=PA\boldsymbol{I = \frac{P}{A}}
Power of a lens
P=1f\boldsymbol{P = \frac{1}{f}}
Lenses in combination
P=P1+P2+P3+…\boldsymbol{P = P_1 + P_2 + P_3 + \dots}
Thin lens equation
1u+1v=1f\boldsymbol{\frac{1}{u} + \frac{1}{v} = \frac{1}{f}}
Magnification for a lens
m=vu\boldsymbol{m = \frac{v}{u}}
Diffraction grating
nλ=dsin⁡θ\boldsymbol{n\lambda = d\sin\theta}
Refractive index (Snell's law)
n1sin⁡θ1=n2sin⁡θ2\boldsymbol{n_1\sin\theta_1 = n_2\sin\theta_2}
Refractive index (speed of light)
n=cv\boldsymbol{n = \frac{c}{v}}
Critical angle
sin⁡C=1n\boldsymbol{\sin C = \frac{1}{n}}
Photon model
E=hf\boldsymbol{E = hf}
Einstein's photoelectric equation
hf=ϕ+12mvmax2\boldsymbol{hf = \phi + \frac{1}{2}mv_{\text{max}}^2}
de Broglie wavelength
λ=hp\boldsymbol{\lambda = \frac{h}{p}}

Further Mechanics Expected Formulas

Further Mechanics Equations

Impulse
FΔt=Δp\boldsymbol{F\Delta t = \Delta p}
Kinetic energy of a non-relativistic particle
Ek=p22m\boldsymbol{E_k = \frac{p^2}{2m}}
Motion in a circle (speed-angular relationship)
v=ωr\boldsymbol{v = \omega r}
Period of circular motion
T=2πω\boldsymbol{T = \frac{2\pi}{\omega}}
Centripetal acceleration (velocity)
a=v2r\boldsymbol{a = \frac{v^2}{r}}
Centripetal acceleration (angular velocity)
a=rω2\boldsymbol{a = r\omega^2}
Centripetal force (velocity)
F=mv2r\boldsymbol{F = \frac{mv^2}{r}}
Centripetal force (angular velocity)
F=mrω2\boldsymbol{F = mr\omega^2}

Fields Expected Formulas

Coulomb's law

Electrostatic force
F=Q1Q24πε0r2\boldsymbol{F = \frac{Q_1 Q_2}{4\pi\varepsilon_0 r^2}}

Electric field

Electric field (force per charge)
E=FQ\boldsymbol{E = \frac{F}{Q}}
Electric field (point charge)
E=Q4πε0r2\boldsymbol{E = \frac{Q}{4\pi\varepsilon_0 r^2}}
Electric field (uniform parallel plates)
E=Vd\boldsymbol{E = \frac{V}{d}}

Electric potential

Electric potential
V=Q4πε0r\boldsymbol{V = \frac{Q}{4\pi\varepsilon_0 r}}

Capacitance

Capacitance
C=QV\boldsymbol{C = \frac{Q}{V}}

Energy stored in capacitor

Energy stored in capacitor (charge-voltage)
W=12QV\boldsymbol{W = \frac{1}{2}QV}
Energy stored in capacitor (capacitance-voltage)
W=12CV2\boldsymbol{W = \frac{1}{2}CV^2}
Energy stored in capacitor (charge-capacitance)
W=12Q2C\boldsymbol{W = \frac{1}{2}\frac{Q^2}{C}}

Capacitor discharge

Capacitor discharge (charge)
Q=Q0e−t/RC\boldsymbol{Q = Q_0 e^{-t/RC}}

Resistor-capacitor discharge

Resistor-capacitor discharge (current)
I=I0e−t/RC\boldsymbol{I = I_0 e^{-t/RC}}
Resistor-capacitor discharge (voltage)
V=V0e−t/RC\boldsymbol{V = V_0 e^{-t/RC}}
Resistor-capacitor discharge (log charge)
ln⁡Q=ln⁡Q0−tRC\boldsymbol{\ln Q = \ln Q_0 - \frac{t}{RC}}
Resistor-capacitor discharge (log current)
ln⁡I=ln⁡I0−tRC\boldsymbol{\ln I = \ln I_0 - \frac{t}{RC}}
Resistor-capacitor discharge (log voltage)
ln⁡V=ln⁡V0−tRC\boldsymbol{\ln V = \ln V_0 - \frac{t}{RC}}

In a magnetic field

Force on current-carrying conductor
F=BIlsin⁡θ\boldsymbol{F = BIl\sin\theta}
Force on moving charge
F=Bqvsin⁡θ\boldsymbol{F = Bqv\sin\theta}

Faraday's and Lenz's Laws

Induced EMF
E=−d(Nϕ)dt\boldsymbol{\mathcal{E} = -\frac{d(N\phi)}{dt}}

Root-mean-square values

Root-mean-square voltage
Vrms=V02\boldsymbol{V_{\text{rms}} = \frac{V_0}{\sqrt{2}}}
Root-mean-square current
Irms=I02\boldsymbol{I_{\text{rms}} = \frac{I_0}{\sqrt{2}}}

Nuclear and particle physics Expected Formulas

In a magnetic field

Radius of path of charged particle
r=pBQ\boldsymbol{r = \frac{p}{BQ}}

Thermodynamics Expected Formulas

Heating

Specific heat capacity
ΔE=mcΔθ\boldsymbol{\Delta E = mc\Delta\theta}
Specific latent heat
ΔE=LΔm\boldsymbol{\Delta E = L\Delta m}

Molecular kinetic theory

Average kinetic energy of molecule
12m⟨c2⟩=32kT\boldsymbol{\frac{1}{2}m\langle c^2 \rangle = \frac{3}{2}kT}
Pressure-volume relation
pV=13Nm⟨c2⟩\boldsymbol{pV = \frac{1}{3}Nm\langle c^2 \rangle}

Ideal gas equation

Ideal gas equation
pV=NkT\boldsymbol{pV = NkT}

Stefan-Boltzmann law

Stefan-Boltzmann law (luminosity-temperature-area)
L=σT4A\boldsymbol{L = \sigma T^4 A}
Stefan-Boltzmann law (radial source)
L=4πr2σT4\boldsymbol{L = 4\pi r^2\sigma T^4}

Wien's law

Wien's displacement law
\boldsymbol{\lambda_{\text{max}}T = 2.898 \times 10^{-3}\ \text{m}\ \text{K}

Space Expected Formulas

Radiant energy flux

Radiant energy flux
I=L4πd2\boldsymbol{I = \frac{L}{4\pi d^2}}

Redshift of electromagnetic radiation

Redshift
z=Δλλ≈Δff≈vc\boldsymbol{z = \frac{\Delta\lambda}{\lambda} \approx \frac{\Delta f}{f} \approx \frac{v}{c}}

Cosmological expansion

Hubble's law
v=H0d\boldsymbol{v = H_0 d}

Nuclear radiation Expected Formulas

Mass-energy

Mass-energy equivalence
ΔE=c2Δm\boldsymbol{\Delta E = c^2\Delta m}

Radioactive decay

Radioactive decay activity
A=λN\boldsymbol{A = \lambda N}
Radioactive decay rate
dNdt=−λN\boldsymbol{\frac{dN}{dt} = -\lambda N}
Decay constant
λ=ln⁡2t1/2\boldsymbol{\lambda = \frac{\ln 2}{t_{1/2}}}
Radioactive decay (number of nuclei remaining)
N=N0e−λt\boldsymbol{N = N_0 e^{-\lambda t}}
Radioactive decay (activity remaining)
A=A0e−λt\boldsymbol{A = A_0 e^{-\lambda t}}

Gravitational fields Expected Formulas

Gravitational force

Newton's law of universal gravitation
F=Gm1m2r2\boldsymbol{F = \frac{Gm_1m_2}{r^2}}

Gravitational field

Gravitational field strength
g=Gmr2\boldsymbol{g = \frac{Gm}{r^2}}

Gravitational potential

Gravitational potential in radial field
Vgrav=−Gmr\boldsymbol{V_{\text{grav}} = \frac{-Gm}{r}}

Oscillations Expected Formulas

Simple harmonic motion

Condition for simple harmonic motion
F=−kx\boldsymbol{F = -kx}
SHM acceleration-displacement relation
a=−ω2x\boldsymbol{a = -\omega^2 x}
SHM displacement-time relation
x=Acos⁡ωt\boldsymbol{x = A\cos\omega t}
SHM velocity-time relation
v=−Aωsin⁡ωt\boldsymbol{v = -A\omega\sin\omega t}
SHM acceleration-time relation
a=−Aω2cos⁡ωt\boldsymbol{a = -A\omega^2\cos\omega t}
SHM period relation
T=1f=2πω\boldsymbol{T = \frac{1}{f} = \frac{2\pi}{\omega}}
SHM angular frequency
ω=2πf\boldsymbol{\omega = 2\pi f}

Simple harmonic oscillator

Period of mass-spring system
T=2πmk\boldsymbol{T = 2\pi\sqrt{\frac{m}{k}}}
Period of simple pendulum
T=2πlg\boldsymbol{T = 2\pi\sqrt{\frac{l}{g}}}