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AQA A-Level Physics Data and Formulas, Cheat Sheet of Physics

Essential data and formulas for various physics topics, including fundamental constants, algebraic and geometric equations, astronomical data, electricity, magnetism, mechanics, thermal physics, and nuclear physics. It is intended for use in exams from the June 2017 series onwards.

What you will learn

  • How do geometric equations like the quadratic equation and arc length formula apply in physics?
  • What are the fundamental constants and their values in physics?
  • What is the relationship between electric current, potential difference, and resistance in a circuit?

Typology: Cheat Sheet

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Uploaded on 02/07/2022

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A-level Physics data and formulae
For use in exams from the June 2017 Series onwards
Version 1.5 1
DATA - FUNDAMENTAL CONSTANTS AND VALUES
Quantity Symbol Value Units
speed of light in vacuo
𝑐
3.00
×
108
m s1
permeability of free space
𝜇0
4
π
×
107
H m1
permittivity of free space
𝜀0
8.85
×
1012
F m1
magnitude of the charge of electron
𝑒
1.60
×
1019
C
the Planck constant
6.63
×
1034
J s
gravitational constant
𝐺
6.67
×
1011
N m2 kg2
the Avogadro constant
𝑁A
6.02
×
1023
mol1
molar gas constant
𝑅
8.31
J K1 mol1
the Boltzmann constant
𝑘
1.38
×
1023
J K1
the Stefan constant
σ
5.67
×
108
W m2 K4
the Wien constant
𝛼
2.90
×
103
m K
electron rest mass
(equivalent to
5.5 × 10–4
u)
𝑚e
9.11
×
1031
kg
electron charge/mass ratio
𝑒
𝑚e
1.76
×
1011
C kg1
proton rest mass
(equivalent to
1.00728
u)
𝑚p
1.67(3)
×
1027
kg
proton charge/mass ratio
𝑒
𝑚p
9.58
×
107
C kg1
neutron rest mass
(equivalent to
1.00867
u)
𝑚n
1.67(5)
×
1027
kg
gravitational field strength
𝑔
9.81
N kg1
acceleration due to gravity
𝑔
9.81
m s2
atomic mass unit
(
1
u is equivalent to
931.5
MeV
)
u
1.661
×
1027
kg
ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS
quadratic equation
arc length = r
𝜃
circumference of circle = 2πr
ASTRONOMICAL DATA area of circle = πr2
Body Mass/
kg
Mean radius/
m
curved surface area of
cylinder
= 2πrh
Sun
1.99 × 1030
6.96 × 108
area of sphere = 4πr2
Earth
5.97 × 1024
6.37 × 106
volume of sphere =
3
4
πr3
pf3
pf4
pf5
pf8

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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 𝜇 0 4 π × 10 –^7 H m–^1

permittivity of free space 𝜀 0 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 J s

gravitational constant 𝐺 6. 67 × 10 –^11 N m^2 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 m K

electron rest mass (equivalent to 5.5 × 10–^4 u)

𝑚e 9. 11 × 10 –^31 kg

electron charge/mass ratio

𝑚e

  1. 76 × 1011 C kg–^1

proton rest mass (equivalent to 1.00728 u)

𝑚p 1. 67 ( 3 ) × 10 –^27 kg

proton charge/mass ratio

𝑚p

  1. 58 × 107 C kg–^1

neutron rest mass (equivalent to 1.00867 u)

𝑚n 1. 67 ( 5 ) × 10 –^27 kg

gravitational field strength 𝑔 9. 81 N kg–^1

acceleration due to gravity 𝑔 9. 81 m s–^2

atomic mass unit ( 1 u is equivalent to 931.5 MeV)

u 1. 661 × 10 –^27 kg

ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS

quadratic equation a

x b b ac 2

2

arc length = r 𝜃

circumference of circle = 2π r

ASTRONOMICAL DATA area of circle^ =^ π r

2

Body Mass/kg Mean radius/m

curved surface area of cylinder

= 2π rh

Sun 1. 99 × 1030 6. 96 × 108 area of sphere = 4π r^2

Earth 5. 97 × 1024 6. 37 × 106 volume of sphere^ =^3

4

π r^3

Particle Physics

Class Name Symbol Rest energy/MeV

photon photon 𝛾 (^0)

lepton neutrino v e 0

v μ 0

electron e ±^ 0.

muon μ±^ 105.

mesons π meson π±^ 139.

π^0 134.

K meson K±^ 493.

K

0

baryons proton p 938.

neutron (^) n 939.

Properties of quarks

antiquarks have opposite signs

Type Charge

Baryon number

Strangeness

u +

3

2

e +^

3

1

d −^

3

1

e +

3

1

s −^

3

1

e +

3

1

Properties of Leptons

Lepton number

Particles: e

e ;^ μ

Antiparticles: e+, νe, μ+, ν μ − 1

Photons and energy levels

photon energy (^) 𝐸 = ℎ𝑓 =

photoelectricity ℎ𝑓^ =^ ϕ^ +^ 𝐸k (max)

energy levels (^) ℎ𝑓 = 𝐸 1 – 𝐸 2

de Broglie wavelength (^) 𝜆 =

Waves

wave speed (^) 𝑐 = 𝑓𝜆 period (^) 𝑓 =

first harmonic 𝑓^ =^

fringe spacing 𝑤^ =^

diffraction grating 𝑑 sin 𝜃 = 𝑛𝜆

refractive index of a substance s , 𝑛 = 𝑐 𝑐s for two different substances of refractive indices n 1 and n 2 , law of refraction 𝑛 1 sin 𝜃 1 = 𝑛 2 sin 𝜃 2

critical angle sin 𝜃c =

𝑛 2 𝑛 1

for 𝑛 1 > 𝑛 2

Mechanics

moments moment = 𝐹𝑑

velocity and acceleration 𝑚^ =^

equations of motion

𝑚^2 = 𝑢^2 + 2 𝑎𝑠 𝑠 = 𝑢𝑡 +
𝑎𝑡^2

force (^) 𝐹 = 𝑚𝑎

force (^) 𝐹 =

impulse 𝐹 Δ𝑡 = Δ(𝑚𝑚) work, energy and power

𝑊 = 𝐹 𝑠 cos 𝜃

𝐸k =

𝑚 𝑚^2 Δ𝐸p =^ 𝑚𝑔Δℎ

∆𝑊 ∆𝑡 ,^ 𝑃^ =^ 𝐹𝑚

𝑒𝑓𝑓𝑒𝑐𝑒𝑒𝑛𝑐𝑒 =

Materials

density 𝜌 =

𝑚 𝑉

Hooke’s law 𝐹 = 𝑘 Δ𝐿

Young modulus =

𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑡𝑡𝑡 𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑠𝑡𝑛

tensile stress =

𝐹 𝐴

tensile strain =

∆𝐿 𝐿

energy stored 𝐸 =

1 2

Magnetic fields

force on a current 𝐹 = 𝐵𝐼𝑙 force on a moving charge 𝐹 = 𝐵𝑄𝑚

magnetic flux Ф = 𝐵𝑅 magnetic flux linkage 𝑁 Ф = 𝐵𝑅𝑁 cos 𝜃

magnitude of induced emf (^) 𝜀 = 𝑁

Δ Ф

𝑁 Ф = 𝐵𝑅𝑁 cos 𝜃 emf induced in a rotating coil 𝜀 = 𝐵𝑅𝑁𝜔 sin 𝜔 t

alternating current 𝐼rms =

𝑉rms =

transformer equations

𝑁s 𝑁p

𝑉s 𝑉p

efficiency =

𝐼s𝑉s

𝐼p𝑉p

Nuclear physics

inverse square law for γ radiation (^) 𝐼 =

𝑥^2

radioactive decay Δ𝑁 Δ𝑡

= – 𝜆 𝑁 , 𝑁 = 𝑁oe−𝜆𝑡

activity 𝑅 = 𝜆𝑁

half-life (^) 𝑇½ =

ln 2 𝜆 nuclear radius (^) 𝑅 = 𝑅 0 𝑅^1 /^3

energy-mass equation 𝐸 = 𝑚𝑐^2

OPTIONS

Astrophysics

1 astronomical unit = 1. 50 × 1011 m

1 light year = 9. 46 × 1015 m 1 parsec = 2. 06 × 105 AU = 3. 08 × 1016 m = 3. 26 ly

Hubble constant, 𝐻 = 65 km s–^1 Mpc–^1

telescope in normal adjustment

𝑓e

Rayleigh criterion (^) 𝜃 ≈

magnitude equation (^) 𝑚 – 𝐺 = 5 log

Wien’s law 𝜆max 𝑇 = 2. 9 × 10 −^3 m K

Stefan’s law (^) 𝑃 = 𝜎𝑅𝑇^4

Schwarzschild radius 𝑅s ≈ (^2)

2 c

GM

Doppler shift for v << c

red shift (^) 𝑧 = −

Hubble’s law (^) 𝑚 = 𝐻𝑑

Medical physics

lens equations 𝑃^ =^

1 𝑓

1 𝑢

1 𝑣 threshold of hearing (^) 𝐼 0 = 1. 0 × 10 −^12 W m−^2

intensity level 𝑒𝑛𝑡𝑒𝑛𝑠𝑒𝑡𝑒 𝑙𝑒𝑚𝑒𝑙 = 10 log

absorption (^) 𝐼 = 𝐼 0 𝑒–𝜇𝜇

𝜇m =

ultrasound imaging (^) 𝑍 = 𝑝 𝑐

𝐼r 𝐼i

𝑍 2 − 𝑍 1 𝑍 2 + 𝑍 1

2

half-lives

1 𝑇E

𝑇B
𝑇P

AQA A-LEVEL PHYSICS DATA AND FORMULAE

Engineering physics

moment of inertia 𝐼 = Σ𝑚𝑝^2

angular kinetic energy (^) 𝐸𝑘 =

𝐼𝜔^2

equations of angular motion 𝜔 2 = 𝜔 1 + 𝛼 𝑡

𝜔 22 = 𝜔 12 + 2 𝛼𝜃

𝛼𝑡^2

torque 𝑇 = 𝐼 𝛼 𝑇 = 𝐹 𝑝 angular momentum (^) 𝑎𝑛𝑔𝑢𝑙𝑎𝑝 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 = 𝐼𝜔

angular impulse 𝑇Δ𝑡 = Δ(𝐼𝜔) work done 𝑊 = 𝑇𝜃 power (^) 𝑃 = 𝑇𝜔

thermodynamics 𝑄 = Δ𝑈 + 𝑊 𝑊 = 𝑝Δ𝑉 adiabatic change (^) 𝑝𝑉𝛾^ = constant

isothermal change 𝑝𝑉 = constant heat engines

efficiency =

𝑄H
𝑄H − 𝑄C
𝑄H

maximum theoretical efficiency =

𝑇H − 𝑇C
𝑇H

work done per cycle = area of loop

input power = calorific value × fuel flow rate indicated power = (𝑎𝑝𝑒𝑎 𝑜𝑓 𝑝 − 𝑉 𝑙𝑜𝑜𝑝) × (𝑛𝑢𝑚𝑠𝑒𝑝 𝑜𝑓 𝑐𝑒𝑐𝑙𝑒𝑠 𝑝𝑒𝑝 𝑠𝑒𝑐𝑜𝑛𝑑) × (𝑛𝑢𝑚𝑠𝑒𝑝 𝑜𝑓 𝑐𝑒𝑙𝑒𝑛𝑑𝑒𝑝𝑠)

output or brake power 𝑃 = 𝑇𝜔

friction power = 𝑒𝑛𝑑𝑒𝑐𝑎𝑡𝑒𝑑 𝑝𝑜𝑤𝑒𝑝 – 𝑠𝑝𝑎𝑘𝑒 𝑝𝑜𝑤𝑒𝑝 heat pumps and refrigerators

refrigerator: 𝐶𝐶𝑃ref =

𝑄C 𝑊

𝑄C 𝑄H− 𝑄C

heat pum p : 𝐶𝐶𝑃hp =

𝑄H 𝑊

𝑄H 𝑄H− 𝑄C

Turning points in physics

electrons in fields (^) 𝐹 =

½ 𝑚𝑚^2 = 𝑒𝑉

Millikan’s experiment

Maxwell’s formula 𝑐^ =^

√^2 𝑚𝑒𝑉

special relativity 𝑡^ =^

2 𝑐 2

𝑚^2
𝑐^2
𝐸 = 𝑚 𝑐^2 =
𝑚 0 𝑐^2

2 𝑐 2

Electronics

resonant frequency 𝑓 0 =

Q-factor 𝑄 =

𝑓B

operational amplifiers: open loop 𝑉out =^ 𝑅OL(𝑉+ −^ 𝑉−) inverting amplifier 𝑉out 𝑉in

𝑅f 𝑅in non-inverting amplifier 𝑉out 𝑉in

𝑅f 𝑅l summing amplifier 𝑉out = −𝑅f �

difference amplifier 𝑉out = (𝑉+ − 𝑉−)

𝑅f 𝑅l

Bandwidth requirement: for AM 𝑠𝑎𝑛𝑑𝑤𝑒𝑑𝑡ℎ = 2 𝑓M for FM (^) 𝑠𝑎𝑛𝑑𝑤𝑒𝑑𝑡ℎ = 2 (∆𝑓 + 𝑓M)

AQA A-LEVEL PHYSICS DATA AND FORMULAE

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