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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
Typology: Cheat Sheet
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electron rest mass (equivalent to 5.5 × 10–^4 u)
electron charge/mass ratio
proton rest mass (equivalent to 1.00728 u)
proton charge/mass ratio
neutron rest mass (equivalent to 1.00867 u)
atomic mass unit ( 1 u is equivalent to 931.5 MeV)
quadratic equation a
x b b ac 2
2
2
Body Mass/kg Mean radius/m
curved surface area of cylinder
4
Class Name Symbol Rest energy/MeV
photon photon 𝛾 (^0)
0
baryons proton p 938.
neutron (^) n 939.
antiquarks have opposite signs
Type Charge
Baryon number
Strangeness
3
2
3
1
3
1
3
1
3
1
3
1
Lepton number
photon energy (^) 𝐸 = ℎ𝑓 =
photoelectricity ℎ𝑓^ =^ ϕ^ +^ 𝐸k (max)
energy levels (^) ℎ𝑓 = 𝐸 1 – 𝐸 2
de Broglie wavelength (^) 𝜆 =
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
𝑛 2 𝑛 1
moments moment = 𝐹𝑑
velocity and acceleration 𝑚^ =^
equations of motion
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 =
𝑚 𝑉
Hooke’s law 𝐹 = 𝑘 Δ𝐿
Young modulus =
𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑡𝑡𝑡 𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑠𝑡𝑛
tensile stress =
𝐹 𝐴
tensile strain =
∆𝐿 𝐿
1 2
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
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
inverse square law for γ radiation (^) 𝐼 =
radioactive decay Δ𝑁 Δ𝑡
activity 𝑅 = 𝜆𝑁
half-life (^) 𝑇½ =
ln 2 𝜆 nuclear radius (^) 𝑅 = 𝑅 0 𝑅^1 /^3
energy-mass equation 𝐸 = 𝑚𝑐^2
OPTIONS
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
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
moment of inertia 𝐼 = Σ𝑚𝑝^2
angular kinetic energy (^) 𝐸𝑘 =
equations of angular motion 𝜔 2 = 𝜔 1 + 𝛼 𝑡
𝜔 22 = 𝜔 12 + 2 𝛼𝜃
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 =
maximum theoretical efficiency =
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
𝑄C 𝑊
𝑄C 𝑄H− 𝑄C
𝑄H 𝑊
𝑄H 𝑄H− 𝑄C
electrons in fields (^) 𝐹 =
Millikan’s experiment
Maxwell’s formula 𝑐^ =^
special relativity 𝑡^ =^
2 𝑐 2
2 𝑐 2
resonant frequency 𝑓 0 =
Q-factor 𝑄 =
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)