1. A Level Physics Formulae
10. Creating models
Radioactivity
Probability p of decay in time ∆t: p = λ ∆t
dN
Activity: = −λ N
dt
Number of atoms: N = N 0 e− λt
ln 2
Half-life: t1/ 2 =
λ
Exponential decay of charge
dQ Q
Change in discharge: =−
dt RC
Discharge of capacitor: Q = Q0 e − t / RC
Time constant (charge reduced by 1/e): τ = RC
Charge, capacitance and voltage: Q = CV
1 1 1 Q2
Energy stored on capacitor: E = QV = CV 2 = ⋅
2 2 2 C
Harmonic oscillators
2π m
Period of harmonic oscillator: T= = 2π
ω k
l
Period of pendulum of length l: T = 2π
g
d 2s k
= − s = − ( 2π f ) s
2
Acceleration ∝ displacement: 2
dt m
Displacement, where φ is phase angle: s = A sin ( 2π ft + φ ) , i.e. ω = 2π f
1 2 1 2
Energy stored in mechanical oscillator: E= kx + mv
2 2

2. 11. Out into space
mv 2
Centripetal force: F= = mω 2 r
r
Gm1m2
Gravitational force between two masses: F =−
r2
GM
Gravitational field strength: g=−
r2
G.P.E. difference in uniform field: E = mg ∆h
GM
Gravitational potential: Vgrav = −
r
∆p ∆v
Force, momentum and acceleration: F= =m = ma
∆t ∆t
12. Our place in the Universe
v ∆tback − ∆tout
Relative velocity from radar: =
c ∆tback + ∆tout
v λback − λout ∆λ v
Doppler shift (two-way): = ⇒ ≈
c λback + λout 2λ c
∆λ v
Doppler shift (one-way): ≈
λ c
Recession velocity: v = H 0r
Robserved ∆λ
Red-shift: = 1+ = 1+ z
Remitted λemitted
13. Matter: very simple
p1V1 p2V2
Ideal gas law: pV = nRT = NkT ⇒ =
T1 T2
1
Kinetic model of a gas: pV = Nmc 2
3
1 2 3
Average kinetic energy of molecule: mv = kT
2 2
3 3
Internal energy of monatomic gas: U= NkT = nRT
2 2
Internal energy, work, thermal transfer: ∆U = W + Q
Change in energy: ∆E = m c ∆θ

3. Approximate energy of particle: kT
14. Matter: very hot and very cold
Boltzmann factor: exp ( −ε / kT )
Rate of reaction: rate ∝ exp ( −ε / kT )
15. Electromagnetic machines
Flux
Flux linkage: flux linkage = Nφ
φ
Permeance, magnetic flux, current-turns: Λ=
NI
µA
Permeance, area, length: Λ=
L
dφ
Electromotive force: e.m.f. = − N
dt
φ
Flux density: B=
A
Flux density, where n = turns/metre: B = µ nI
Transformers
VS N S
Transformer, voltage & turns: =
VP N P
IS NP
Transformer, current & turns: =
IP NS
Force on conductor: F = ILB
16. Charge and field
Work done: W = q∆V
2qV
Speed of particle: v=
m
F ∆V
Electric field strength (NC-1 or Vm-1): E= =−
q ∆x
E
Electric potential at point in field: V=
q

4. Magnetic force on moving charge: F = qvB
p
Radius of circular path in magnetic field: r=
qB
q
Electric potential: Velec =
4πε 0 r
q
Electric field strength: E=
4πε 0 r 2
q1q2
Force between two point charges: F=
4πε 0 r 2
17. Probing deep into matter
h
De Broglie wavelength: λ=
p
Energy-frequency relationship for photons: E = hf = Einitial − E final
−13.6eV
Energy level spacings in hydrogen: En =
n2
18. Ionising radiation and risk
Exponential attenuation of γ radiation: I = I 0e− µ x
Risk: risk = probability x consequences
E
Absorbed dose (measured in gray): dose =
m
E
Dose (measured in sievert): dose = × quality factor
m
Rest energy: Erest = mc 2
Binding energy of nucleus: E = ( mnucleus − mnucleons ) c 2
General / AS formulae
m
Density, mass and volume: p=
V
Momentum (for slow particles): p = mv
Energy transfer in circuit: E = VIt = Pt = qV
Force, mass and acceleration: F = ma

5. Weight: W = mg
1 2
Kinetic energy: K.E. = mv
2
Change in potential energy: ∆P.E. = mg ∆h
Work done: Work done = Fs
Charge: ∆Q = I ∆t
Potential difference: V = IR
V2
Electrical power: P = IV = I 2 R =
R
V ρL
Resistance: R= =
I A
I σA
Conductance: G= =
V L
Internal resistance: Vload = E − IRinternal
F
Pressure: P=
A
Wave speed: v= fλ
1
Frequency: f =
T
Impulse: Impulse = F ∆t = mv − mu
Fs
Power: P= = Fv
t
useful energy output
Efficiency: Efficiency =
total energy output
s
Speed, distance, time: v=
t
1
Constant acceleration formulae: s = ut + at 2
2
v = u + at
v 2 = u 2 + 2as
1 1 1 sin i cvacuum
Optics: = + ; n= =
v u f sin r cmedium