A-level Physics data and formulae
For use in exams from the June 2017 Series onwards
DATA - FUNDAMENTAL CONSTANTS AND VALUES
Quantity Symbol Value Units
speed of light in vacuo 𝑐 3.00 × 108 m s –1
permeability of free space 𝜇0 4π × 10–7 H m–1
permittivity of free space 𝜀0 8.85 × 10–12 F m–1
magnitude of the charge of electron 𝑒 1.60 × 10–19 C
the Planck constant ℎ 6.63 × 10–34 Js
gravitational constant 𝐺 6.67 × 10–11 N m2 kg –2
the Avogadro constant 𝑁A 6.02 × 1023 mol–1
molar gas constant 𝑅 8.31 J K –1 mol–1
the Boltzmann constant 𝑘 1.38 × 10–23 J K –1
the Stefan constant σ 5.67 × 10–8 W m–2 K –4
the Wien constant 𝛼 2.90 × 10–3 mK
electron rest mass
𝑚e 9.11 × 10–31 kg
(equivalent to 5.5 × 10–4 u)
𝑒
magnitude of electron charge/mass ratio 1.76 × 1011 C kg –1
𝑚e
proton rest mass 𝑚p 1.67(3) × 10–27 kg
(equivalent to 1.00728 u)
𝑒
proton charge/mass ratio 9.58 × 107 C kg –1
𝑚p
neutron rest mass
𝑚n 1.67(5) × 10–27 kg
(equivalent to 1.00867 u)
gravitational field strength 𝑔 9.81 N kg –1
acceleration due to gravity 𝑔 9.81 m s –2
atomic mass unit u 1.661 × 10–27 kg
(1u is equivalent to 931.5 MeV)
ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS
arc length = r𝜃
− b ± b 2 − 4 ac
quadratic equation x=
2a circumference of circle = 2πr
ASTRONOMICAL DATA area of circle = πr2
curved surface area of = 2πrh
Body Mass/kg Mean radius/m
cylinder
Sun 1.99 × 1030 6.96 × 108 surface area of sphere = 4πr2
4
Earth 5.97 × 1024 6.37 × 106 volume of sphere = πr3
3
Version 1.7 1
,Particle Physics Waves
Class Name Symbol Rest energy/MeV 1
wave speed 𝑐 = 𝑓𝑓 period 𝑓 =
𝑇
photon photon 𝛾 0
first 1 𝑇
lepton neutrino ve 0 𝑓 = �
harmonic 2𝑙 𝜇
vµ 0
fringe 𝜆𝜆 diffraction
electron e± 0.510999 𝑤 = 𝑑 sin 𝜃 = 𝑛𝑛
spacing 𝑠 grating
muon µ± 105.659 refractive index of a substance s, 𝑛 =
𝑐
𝑐s
mesons π meson π± 139.576
for two different substances of refractive indices n1 and n2,
π0
134.972 law of refraction 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
± 𝑛2
K meson K 493.821 critical angle sin 𝜃c = for 𝑛1 > 𝑛2
𝑛1
0
K 497.762
baryons proton p 938.257 Mechanics
neutron n 939.551 moments moment = 𝐹𝐹
velocity and ∆𝑠 ∆𝑣
Properties of quarks 𝑣 = 𝑎 =
acceleration ∆𝑡 ∆𝑡
antiquarks have opposite signs
equations of 𝑢+𝑣
𝑣 = 𝑢 + 𝑎𝑎 𝑠 =� �𝑡
Baryon motion 2
Type Charge Strangeness
number 𝑎𝑎 2
𝑣 2 = 𝑢2 + 2𝑎𝑎 𝑠 = 𝑢𝑢 +
2
2 1
u + e + 0 force 𝐹 = 𝑚𝑚
3 3
∆(𝑚𝑚)
1 force 𝐹 =
d − e + 1
0 ∆𝑡
3 3
impulse 𝐹 Δ𝑡 = Δ(𝑚𝑚)
1
s − e + 1
−1 work, energy 𝑊 = 𝐹 𝑠 cos 𝜃
3 3 and power
1
𝐸k = 𝑚 𝑣2 Δ𝐸p = 𝑚𝑚Δℎ
2
Properties of Leptons ∆𝑊
𝑃 = ∆𝑡
, 𝑃 = 𝐹𝐹
Lepton number
𝑢𝑢𝑢𝑢𝑢𝑢 𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝
Particles: e− , νe ; µ− , νµ +1 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 =
𝑖𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝
Antiparticles: e+ , ν e , µ + , ν µ −1
Materials
𝑚
Photons and energy levels density 𝜌 = Hooke’s law 𝐹 = 𝑘 Δ𝐿
𝑉
ℎ𝑐 𝐹
photon energy 𝐸 = ℎ𝑓 = tensile stress =
𝜆 𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠 𝐴
Young modulus =
photoelectricity ℎ𝑓 = ϕ + 𝐸k (max) 𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠 ∆𝐿
tensile strain =
𝐿
energy levels ℎ𝑓 = 𝐸1 – 𝐸2
1
ℎ ℎ energy stored 𝐸 = 2 𝐹Δ𝐿
de Broglie wavelength 𝜆 = =
𝑝 𝑚𝑚
2 Version 1.7
, AQA A-LEVEL PHYSICS DATA AND FORMULAE
Electricity Gravitational fields
∆𝑄 𝑊 𝑉 𝐺𝑚1 𝑚2
current and pd 𝐼 = 𝑉 = 𝑅 = force between two masses 𝐹 =
∆𝑡 𝑄 𝐼 𝑟2
𝑅𝑅 𝐹
resistivity 𝜌= gravitational field strength 𝑔 =
𝐿 𝑚
resistors in series 𝑅T = 𝑅1 + 𝑅2 + 𝑅3 + … magnitude of gravitational 𝐺𝐺
field strength in a radial field 𝑔 =
𝑟2
1 1 1 1
resistors in parallel = + + +⋯ work done Δ𝑊 = 𝑚Δ𝑉
𝑅T 𝑅1 𝑅2 𝑅3
𝐺𝐺
2
gravitational potential 𝑉 =–
𝑉 𝑟
power 𝑃 = 𝑉𝑉 = 𝐼 2 𝑅 = Δ𝑉
𝑅 𝑔 =–
𝐸 Δ𝑟
emf 𝜀 = 𝜀 = 𝐼(𝑅 + 𝑟)
𝑄
Electric fields and capacitors
Circular motion
force between two 1 𝑄1 𝑄2
𝐹 =
magnitude of 𝑣 point charges 4𝜋𝜀0 𝑟 2
𝜔 =
angular speed 𝑟 force on a charge 𝐹 = 𝐸𝐸
𝜔 = 2𝜋𝜋 𝑉
field strength for a
𝐸 =
𝑣2 uniform field 𝑑
centripetal acceleration 𝑎 = = 𝜔2 𝑟
𝑟 work done Δ𝑊 = 𝑄Δ𝑉
𝑚𝑚 2
centripetal force 𝐹 = = 𝑚𝑚2 𝑟
𝑟 field strength for a 1 𝑄
𝐸 =
Simple harmonic motion
radial field 4𝜋𝜀0 𝑟 2
1 𝑄
acceleration 𝑎 = − 𝜔2 𝑥 electric potential 𝑉 =
4𝜋𝜀0 𝑟
displacement 𝑥 = 𝐴 cos (𝜔𝜔) Δ𝑉
field strength 𝐸 =
speed 𝑣 = ±𝜔 �(𝐴2 − 𝑥 2) Δ𝑟
𝑄
maximum speed 𝑣max = 𝜔𝜔 capacitance 𝐶 =
𝑉
2
maximum acceleration 𝑎max = 𝜔 𝐴 𝐴𝜀0 𝜀r
𝑚 𝐶 =
𝑑
for a mass-spring system 𝑇 = 2𝜋 �
𝑘 capacitor energy 1 1 1 𝑄2
stored 𝐸 = 𝑄𝑄 = 𝐶𝑉 2 =
𝑙 2 2 2 𝐶
for a simple pendulum 𝑇 = 2𝜋 � capacitor charging 𝑡
𝑔 𝑄 = 𝑄0 (1 − e– 𝑅𝑅 )
Thermal physics decay of charge 𝑄 = 𝑄0 e– 𝑅𝑅
𝑡
energy to change
𝑄 = 𝑚𝑚Δ𝜃
time constant 𝑅𝑅
temperature
energy to change
𝑄 = 𝑚𝑚
state
gas law 𝑝𝑝 = 𝑛𝑛𝑛
𝑝𝑝 = 𝑁𝑁𝑁
1
kinetic theory model 𝑝𝑝 = 𝑁𝑁 (𝑐rms )2
3
kinetic energy of gas 1 3 3𝑅𝑅
𝑚 (𝑐rms )2 = 𝑘𝑘 =
molecule 2 2 2𝑁A
Version 1.7 3
,Magnetic fields OPTIONS
force on a current 𝐹 = 𝐵𝐵𝐵
Astrophysics
force on a moving charge 𝐹 = 𝐵𝐵𝐵
magnetic flux Ф = 𝐵𝐵 1 astronomical unit = 1.50 × 1011 m
magnetic flux linkage 𝑁Ф = 𝐵𝐵𝐵 cos 𝜃 1 light year = 9.46 × 1015 m
ΔФ 1 parsec = 2.06 × 105 AU = 3.08 × 1016 m
magnitude of induced emf 𝜀 = 𝑁 = 3.26 ly
Δ𝑡
𝑁Ф = 𝐵𝐵𝐵 cos 𝜃 Hubble constant, 𝐻 = 65 km s–1 Mpc–1
emf induced in a rotating coil 𝜀 = 𝐵𝐵𝐵𝐵 sin 𝜔 t 𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑏𝑏 𝑖𝑖𝑖𝑖𝑖 𝑎𝑎 𝑒𝑒𝑒
𝑀 =
𝐼0 𝑉0 𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑏𝑏 𝑜𝑜𝑜𝑜𝑜𝑜 𝑎𝑎 𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑒𝑒𝑒
alternating current 𝐼rms = 𝑉rms =
√2 √2 telescope in normal 𝑓0
𝑀 =
𝑁s 𝑉s adjustment 𝑓e
transformer equations =
𝑁p 𝑉p 𝜆
Rayleigh criterion 𝜃 ≈
𝐼s 𝑉s 𝐷
efficiency = 𝑑
𝐼p 𝑉p magnitude equation 𝑚 – 𝑀 = 5 log
10
Nuclear physics Wien’s law 𝜆max 𝑇 = 2.9 × 10−3 m K
𝑘 Stefan’s law 𝑃 = 𝜎𝜎𝑇 4
inverse square law for γ radiation 𝐼 =
𝑥2
2GM
Δ𝑁 Schwarzschild radius 𝑅s ≈
radioactive decay = – 𝜆 𝑁, 𝑁 = 𝑁o e −𝜆𝜆
c2
Δ𝑡
activity 𝐴 = 𝜆𝜆 Δ𝑓 Δ𝜆 𝑣
Doppler shift for v << c =– =
𝑓 𝜆 𝑐
ln 2
half-life 𝑇½ = 𝑣
𝜆 red shift 𝑧= −
𝑐
nuclear radius 𝑅 = 𝑅0 𝐴1/3 Hubble’s law 𝑣 = 𝐻𝐻
2
energy-mass equation 𝐸 = 𝑚𝑚
Medical physics
1
lens equations 𝑃 =
𝑓
𝑣
𝑚 =
𝑢
1 1 1
= +
𝑓 𝑢 𝑣
threshold of hearing 𝐼0 = 1.0 × 10−12 W m−2
𝐼
intensity level 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑙𝑙𝑙𝑙𝑙 = 10 log
𝐼0
absorption 𝐼 = 𝐼0 𝑒 –𝜇𝜇
𝜇
𝜇m =
𝜌
ultrasound imaging 𝑍 = 𝑝𝑐
𝐼r 𝑍2 − 𝑍1 2
= � �
𝐼i 𝑍2 + 𝑍1
1 1 1
half-lives = +
𝑇E 𝑇B 𝑇P
4 Version 1.7
, AQA A-LEVEL PHYSICS DATA AND FORMULAE
Engineering physics Turning points in physics
moment of inertia 𝐼 = Σ𝑚𝑚 2 𝑒𝑒
electrons in fields 𝐹 =
1 2 𝑑
angular kinetic energy 𝐸𝑘 = 𝐼𝐼 𝐹 = 𝐵𝐵𝐵
2
equations of angular 𝑚𝑚
𝑟 =
motion 𝜔2 = 𝜔1 + 𝛼 𝑡 𝐵𝐵
½ 𝑚𝑚 2 = 𝑒𝑒
𝜔2 2 = 𝜔1 2 + 2𝛼𝛼
𝑄𝑄
2 Millikan’s experiment = 𝑚𝑚
𝛼𝛼 𝑑
𝜃 = 𝜔1 𝑡 +
2 𝐹 = 6𝜋𝜋𝜋𝜋
(𝜔1 + 𝜔2 ) 𝑡
𝜃 = 1
2 Maxwell’s formula 𝑐 =
�𝜇0 𝜀0
torque 𝑇 = 𝐼𝛼
𝑇 = 𝐹𝑟 ℎ ℎ
𝜆 = =
𝑝 √2𝑚𝑚𝑚
angular momentum 𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝐼𝐼
𝑡0
angular impulse 𝑇Δ𝑡 = Δ(𝐼𝐼) special relativity 𝑡 =
2
work done 𝑊 = 𝑇𝑇 �1 − 𝑣2
𝑐
power 𝑃 = 𝑇𝑇
thermodynamics 𝑄 = Δ𝑈 + 𝑊 𝑣2
𝑙 = 𝑙0 �1 −
𝑊 = 𝑝Δ𝑉 𝑐2
adiabatic change 𝑝𝑝 𝛾 = constant 𝑚0 𝑐 2
𝐸 = 𝑚 𝑐2 =
2
isothermal change 𝑝𝑝 = constant �1 − 𝑣2
𝑐
heat engines
𝑊 𝑄H − 𝑄C
efficiency = = Electronics
𝑄H 𝑄H
maximum theoretical 𝑇H − 𝑇C resonant frequency 1
𝑓0 =
efficiency = 𝑇H 2𝜋 √𝐿𝐿
work done per cycle = area of loop Q-factor 𝑓0
𝑄=
𝑓B
input power = calorific value × fuel flow rate
operational amplifiers:
indicated power = (𝑎𝑎𝑎𝑎 𝑜𝑜 𝑝 − 𝑉 𝑙𝑙𝑙𝑙) 𝑉out = 𝐴OL (𝑉+ − 𝑉− )
open loop
× (𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜 𝑐𝑐𝑐𝑐𝑐𝑐 𝑝𝑝𝑝 𝑠𝑠𝑠𝑠𝑠𝑠)
× (𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐) inverting amplifier 𝑉out 𝑅f
=−
𝑉in 𝑅in
output or brake power 𝑃 = 𝑇𝜔
non-inverting amplifier 𝑉out 𝑅f
friction power = 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝 – 𝑏𝑏𝑏𝑏𝑏 𝑝𝑝𝑝𝑝𝑝 =1+
𝑉in 𝑅l
heat pumps and refrigerators summing amplifier 𝑉1 𝑉2 𝑉3
𝑉out = −𝑅f � + + + ⋯�
𝑄C 𝑄C 𝑅1 𝑅2 𝑅3
refrigerator: 𝐶𝐶𝐶ref = =
𝑊 𝑄H − 𝑄C difference amplifier 𝑅f
𝑉out = (𝑉+ − 𝑉− )
𝑄H 𝑄H 𝑅l
heat pump: 𝐶𝐶𝐶hp = =
𝑊 𝑄H − 𝑄C
Bandwidth requirement:
for AM 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ = 2𝑓M
for FM 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ = 2(∆𝑓 + 𝑓M )
Version 1.7 5
, 6 Version 1.7
For use in exams from the June 2017 Series onwards
DATA - FUNDAMENTAL CONSTANTS AND VALUES
Quantity Symbol Value Units
speed of light in vacuo 𝑐 3.00 × 108 m s –1
permeability of free space 𝜇0 4π × 10–7 H m–1
permittivity of free space 𝜀0 8.85 × 10–12 F m–1
magnitude of the charge of electron 𝑒 1.60 × 10–19 C
the Planck constant ℎ 6.63 × 10–34 Js
gravitational constant 𝐺 6.67 × 10–11 N m2 kg –2
the Avogadro constant 𝑁A 6.02 × 1023 mol–1
molar gas constant 𝑅 8.31 J K –1 mol–1
the Boltzmann constant 𝑘 1.38 × 10–23 J K –1
the Stefan constant σ 5.67 × 10–8 W m–2 K –4
the Wien constant 𝛼 2.90 × 10–3 mK
electron rest mass
𝑚e 9.11 × 10–31 kg
(equivalent to 5.5 × 10–4 u)
𝑒
magnitude of electron charge/mass ratio 1.76 × 1011 C kg –1
𝑚e
proton rest mass 𝑚p 1.67(3) × 10–27 kg
(equivalent to 1.00728 u)
𝑒
proton charge/mass ratio 9.58 × 107 C kg –1
𝑚p
neutron rest mass
𝑚n 1.67(5) × 10–27 kg
(equivalent to 1.00867 u)
gravitational field strength 𝑔 9.81 N kg –1
acceleration due to gravity 𝑔 9.81 m s –2
atomic mass unit u 1.661 × 10–27 kg
(1u is equivalent to 931.5 MeV)
ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS
arc length = r𝜃
− b ± b 2 − 4 ac
quadratic equation x=
2a circumference of circle = 2πr
ASTRONOMICAL DATA area of circle = πr2
curved surface area of = 2πrh
Body Mass/kg Mean radius/m
cylinder
Sun 1.99 × 1030 6.96 × 108 surface area of sphere = 4πr2
4
Earth 5.97 × 1024 6.37 × 106 volume of sphere = πr3
3
Version 1.7 1
,Particle Physics Waves
Class Name Symbol Rest energy/MeV 1
wave speed 𝑐 = 𝑓𝑓 period 𝑓 =
𝑇
photon photon 𝛾 0
first 1 𝑇
lepton neutrino ve 0 𝑓 = �
harmonic 2𝑙 𝜇
vµ 0
fringe 𝜆𝜆 diffraction
electron e± 0.510999 𝑤 = 𝑑 sin 𝜃 = 𝑛𝑛
spacing 𝑠 grating
muon µ± 105.659 refractive index of a substance s, 𝑛 =
𝑐
𝑐s
mesons π meson π± 139.576
for two different substances of refractive indices n1 and n2,
π0
134.972 law of refraction 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
± 𝑛2
K meson K 493.821 critical angle sin 𝜃c = for 𝑛1 > 𝑛2
𝑛1
0
K 497.762
baryons proton p 938.257 Mechanics
neutron n 939.551 moments moment = 𝐹𝐹
velocity and ∆𝑠 ∆𝑣
Properties of quarks 𝑣 = 𝑎 =
acceleration ∆𝑡 ∆𝑡
antiquarks have opposite signs
equations of 𝑢+𝑣
𝑣 = 𝑢 + 𝑎𝑎 𝑠 =� �𝑡
Baryon motion 2
Type Charge Strangeness
number 𝑎𝑎 2
𝑣 2 = 𝑢2 + 2𝑎𝑎 𝑠 = 𝑢𝑢 +
2
2 1
u + e + 0 force 𝐹 = 𝑚𝑚
3 3
∆(𝑚𝑚)
1 force 𝐹 =
d − e + 1
0 ∆𝑡
3 3
impulse 𝐹 Δ𝑡 = Δ(𝑚𝑚)
1
s − e + 1
−1 work, energy 𝑊 = 𝐹 𝑠 cos 𝜃
3 3 and power
1
𝐸k = 𝑚 𝑣2 Δ𝐸p = 𝑚𝑚Δℎ
2
Properties of Leptons ∆𝑊
𝑃 = ∆𝑡
, 𝑃 = 𝐹𝐹
Lepton number
𝑢𝑢𝑢𝑢𝑢𝑢 𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝
Particles: e− , νe ; µ− , νµ +1 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 =
𝑖𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝
Antiparticles: e+ , ν e , µ + , ν µ −1
Materials
𝑚
Photons and energy levels density 𝜌 = Hooke’s law 𝐹 = 𝑘 Δ𝐿
𝑉
ℎ𝑐 𝐹
photon energy 𝐸 = ℎ𝑓 = tensile stress =
𝜆 𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠 𝐴
Young modulus =
photoelectricity ℎ𝑓 = ϕ + 𝐸k (max) 𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠 ∆𝐿
tensile strain =
𝐿
energy levels ℎ𝑓 = 𝐸1 – 𝐸2
1
ℎ ℎ energy stored 𝐸 = 2 𝐹Δ𝐿
de Broglie wavelength 𝜆 = =
𝑝 𝑚𝑚
2 Version 1.7
, AQA A-LEVEL PHYSICS DATA AND FORMULAE
Electricity Gravitational fields
∆𝑄 𝑊 𝑉 𝐺𝑚1 𝑚2
current and pd 𝐼 = 𝑉 = 𝑅 = force between two masses 𝐹 =
∆𝑡 𝑄 𝐼 𝑟2
𝑅𝑅 𝐹
resistivity 𝜌= gravitational field strength 𝑔 =
𝐿 𝑚
resistors in series 𝑅T = 𝑅1 + 𝑅2 + 𝑅3 + … magnitude of gravitational 𝐺𝐺
field strength in a radial field 𝑔 =
𝑟2
1 1 1 1
resistors in parallel = + + +⋯ work done Δ𝑊 = 𝑚Δ𝑉
𝑅T 𝑅1 𝑅2 𝑅3
𝐺𝐺
2
gravitational potential 𝑉 =–
𝑉 𝑟
power 𝑃 = 𝑉𝑉 = 𝐼 2 𝑅 = Δ𝑉
𝑅 𝑔 =–
𝐸 Δ𝑟
emf 𝜀 = 𝜀 = 𝐼(𝑅 + 𝑟)
𝑄
Electric fields and capacitors
Circular motion
force between two 1 𝑄1 𝑄2
𝐹 =
magnitude of 𝑣 point charges 4𝜋𝜀0 𝑟 2
𝜔 =
angular speed 𝑟 force on a charge 𝐹 = 𝐸𝐸
𝜔 = 2𝜋𝜋 𝑉
field strength for a
𝐸 =
𝑣2 uniform field 𝑑
centripetal acceleration 𝑎 = = 𝜔2 𝑟
𝑟 work done Δ𝑊 = 𝑄Δ𝑉
𝑚𝑚 2
centripetal force 𝐹 = = 𝑚𝑚2 𝑟
𝑟 field strength for a 1 𝑄
𝐸 =
Simple harmonic motion
radial field 4𝜋𝜀0 𝑟 2
1 𝑄
acceleration 𝑎 = − 𝜔2 𝑥 electric potential 𝑉 =
4𝜋𝜀0 𝑟
displacement 𝑥 = 𝐴 cos (𝜔𝜔) Δ𝑉
field strength 𝐸 =
speed 𝑣 = ±𝜔 �(𝐴2 − 𝑥 2) Δ𝑟
𝑄
maximum speed 𝑣max = 𝜔𝜔 capacitance 𝐶 =
𝑉
2
maximum acceleration 𝑎max = 𝜔 𝐴 𝐴𝜀0 𝜀r
𝑚 𝐶 =
𝑑
for a mass-spring system 𝑇 = 2𝜋 �
𝑘 capacitor energy 1 1 1 𝑄2
stored 𝐸 = 𝑄𝑄 = 𝐶𝑉 2 =
𝑙 2 2 2 𝐶
for a simple pendulum 𝑇 = 2𝜋 � capacitor charging 𝑡
𝑔 𝑄 = 𝑄0 (1 − e– 𝑅𝑅 )
Thermal physics decay of charge 𝑄 = 𝑄0 e– 𝑅𝑅
𝑡
energy to change
𝑄 = 𝑚𝑚Δ𝜃
time constant 𝑅𝑅
temperature
energy to change
𝑄 = 𝑚𝑚
state
gas law 𝑝𝑝 = 𝑛𝑛𝑛
𝑝𝑝 = 𝑁𝑁𝑁
1
kinetic theory model 𝑝𝑝 = 𝑁𝑁 (𝑐rms )2
3
kinetic energy of gas 1 3 3𝑅𝑅
𝑚 (𝑐rms )2 = 𝑘𝑘 =
molecule 2 2 2𝑁A
Version 1.7 3
,Magnetic fields OPTIONS
force on a current 𝐹 = 𝐵𝐵𝐵
Astrophysics
force on a moving charge 𝐹 = 𝐵𝐵𝐵
magnetic flux Ф = 𝐵𝐵 1 astronomical unit = 1.50 × 1011 m
magnetic flux linkage 𝑁Ф = 𝐵𝐵𝐵 cos 𝜃 1 light year = 9.46 × 1015 m
ΔФ 1 parsec = 2.06 × 105 AU = 3.08 × 1016 m
magnitude of induced emf 𝜀 = 𝑁 = 3.26 ly
Δ𝑡
𝑁Ф = 𝐵𝐵𝐵 cos 𝜃 Hubble constant, 𝐻 = 65 km s–1 Mpc–1
emf induced in a rotating coil 𝜀 = 𝐵𝐵𝐵𝐵 sin 𝜔 t 𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑏𝑏 𝑖𝑖𝑖𝑖𝑖 𝑎𝑎 𝑒𝑒𝑒
𝑀 =
𝐼0 𝑉0 𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑏𝑏 𝑜𝑜𝑜𝑜𝑜𝑜 𝑎𝑎 𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑒𝑒𝑒
alternating current 𝐼rms = 𝑉rms =
√2 √2 telescope in normal 𝑓0
𝑀 =
𝑁s 𝑉s adjustment 𝑓e
transformer equations =
𝑁p 𝑉p 𝜆
Rayleigh criterion 𝜃 ≈
𝐼s 𝑉s 𝐷
efficiency = 𝑑
𝐼p 𝑉p magnitude equation 𝑚 – 𝑀 = 5 log
10
Nuclear physics Wien’s law 𝜆max 𝑇 = 2.9 × 10−3 m K
𝑘 Stefan’s law 𝑃 = 𝜎𝜎𝑇 4
inverse square law for γ radiation 𝐼 =
𝑥2
2GM
Δ𝑁 Schwarzschild radius 𝑅s ≈
radioactive decay = – 𝜆 𝑁, 𝑁 = 𝑁o e −𝜆𝜆
c2
Δ𝑡
activity 𝐴 = 𝜆𝜆 Δ𝑓 Δ𝜆 𝑣
Doppler shift for v << c =– =
𝑓 𝜆 𝑐
ln 2
half-life 𝑇½ = 𝑣
𝜆 red shift 𝑧= −
𝑐
nuclear radius 𝑅 = 𝑅0 𝐴1/3 Hubble’s law 𝑣 = 𝐻𝐻
2
energy-mass equation 𝐸 = 𝑚𝑚
Medical physics
1
lens equations 𝑃 =
𝑓
𝑣
𝑚 =
𝑢
1 1 1
= +
𝑓 𝑢 𝑣
threshold of hearing 𝐼0 = 1.0 × 10−12 W m−2
𝐼
intensity level 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑙𝑙𝑙𝑙𝑙 = 10 log
𝐼0
absorption 𝐼 = 𝐼0 𝑒 –𝜇𝜇
𝜇
𝜇m =
𝜌
ultrasound imaging 𝑍 = 𝑝𝑐
𝐼r 𝑍2 − 𝑍1 2
= � �
𝐼i 𝑍2 + 𝑍1
1 1 1
half-lives = +
𝑇E 𝑇B 𝑇P
4 Version 1.7
, AQA A-LEVEL PHYSICS DATA AND FORMULAE
Engineering physics Turning points in physics
moment of inertia 𝐼 = Σ𝑚𝑚 2 𝑒𝑒
electrons in fields 𝐹 =
1 2 𝑑
angular kinetic energy 𝐸𝑘 = 𝐼𝐼 𝐹 = 𝐵𝐵𝐵
2
equations of angular 𝑚𝑚
𝑟 =
motion 𝜔2 = 𝜔1 + 𝛼 𝑡 𝐵𝐵
½ 𝑚𝑚 2 = 𝑒𝑒
𝜔2 2 = 𝜔1 2 + 2𝛼𝛼
𝑄𝑄
2 Millikan’s experiment = 𝑚𝑚
𝛼𝛼 𝑑
𝜃 = 𝜔1 𝑡 +
2 𝐹 = 6𝜋𝜋𝜋𝜋
(𝜔1 + 𝜔2 ) 𝑡
𝜃 = 1
2 Maxwell’s formula 𝑐 =
�𝜇0 𝜀0
torque 𝑇 = 𝐼𝛼
𝑇 = 𝐹𝑟 ℎ ℎ
𝜆 = =
𝑝 √2𝑚𝑚𝑚
angular momentum 𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝐼𝐼
𝑡0
angular impulse 𝑇Δ𝑡 = Δ(𝐼𝐼) special relativity 𝑡 =
2
work done 𝑊 = 𝑇𝑇 �1 − 𝑣2
𝑐
power 𝑃 = 𝑇𝑇
thermodynamics 𝑄 = Δ𝑈 + 𝑊 𝑣2
𝑙 = 𝑙0 �1 −
𝑊 = 𝑝Δ𝑉 𝑐2
adiabatic change 𝑝𝑝 𝛾 = constant 𝑚0 𝑐 2
𝐸 = 𝑚 𝑐2 =
2
isothermal change 𝑝𝑝 = constant �1 − 𝑣2
𝑐
heat engines
𝑊 𝑄H − 𝑄C
efficiency = = Electronics
𝑄H 𝑄H
maximum theoretical 𝑇H − 𝑇C resonant frequency 1
𝑓0 =
efficiency = 𝑇H 2𝜋 √𝐿𝐿
work done per cycle = area of loop Q-factor 𝑓0
𝑄=
𝑓B
input power = calorific value × fuel flow rate
operational amplifiers:
indicated power = (𝑎𝑎𝑎𝑎 𝑜𝑜 𝑝 − 𝑉 𝑙𝑙𝑙𝑙) 𝑉out = 𝐴OL (𝑉+ − 𝑉− )
open loop
× (𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜 𝑐𝑐𝑐𝑐𝑐𝑐 𝑝𝑝𝑝 𝑠𝑠𝑠𝑠𝑠𝑠)
× (𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐) inverting amplifier 𝑉out 𝑅f
=−
𝑉in 𝑅in
output or brake power 𝑃 = 𝑇𝜔
non-inverting amplifier 𝑉out 𝑅f
friction power = 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝 – 𝑏𝑏𝑏𝑏𝑏 𝑝𝑝𝑝𝑝𝑝 =1+
𝑉in 𝑅l
heat pumps and refrigerators summing amplifier 𝑉1 𝑉2 𝑉3
𝑉out = −𝑅f � + + + ⋯�
𝑄C 𝑄C 𝑅1 𝑅2 𝑅3
refrigerator: 𝐶𝐶𝐶ref = =
𝑊 𝑄H − 𝑄C difference amplifier 𝑅f
𝑉out = (𝑉+ − 𝑉− )
𝑄H 𝑄H 𝑅l
heat pump: 𝐶𝐶𝐶hp = =
𝑊 𝑄H − 𝑄C
Bandwidth requirement:
for AM 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ = 2𝑓M
for FM 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ = 2(∆𝑓 + 𝑓M )
Version 1.7 5
, 6 Version 1.7
