FORMULAE TO REVISE FOR PSA6

 

FIRST-YEAR UNITS

HFS (Higher, Faster, Stronger)

Velocity

v = Δs / Δt

Acceleration

a = Δv / Δt

Equations of motion

v = u + at

v² = u² + 2as

s = ut + ½at²

s = (u + v)t / 2

Force

F = ma

Kinetic energy

Ek = ½mv²

Gravitational field strength

g = F/m

Weight (force due to gravity)

W = mg

SPC (Technology in Space)

Charge

ΔQ = IΔt

Voltage (potential difference)

V = W / Q

Resistance

R = V / I

Resistance in parallel circuits

Voltage in parallel circuits

Current in parallel circuits

1/R = 1/R1 + 1/R2 + 1/R3

V = V1 = V2 = V3

I = I1 + I2 + I3

Resistance in series circuits

Voltage in series circuits

Current in series circuits

R = R1 + R2 + R3

V = V1 + V2 + V3

I = I1 = I2 = I3

Power

P = I²R

P = V² / R

Efficiency

ε = 100% × useful energy output / energy input

ε = 100% × useful power output / power input

Thermal energy

ΔQ = mcΔθ

Resistance at temperature θ Kelvin

Rθ = R0(1 + αθ)

Rθ= R0 + αR0θ

MUS (The Sound of Music)

Wave equation

v = fλ

Speed of a wave on a string or wire

v = √(T / μ)

Photon energy

E = hf

DIG (Digging up the Past)

Resistance

R = ρℓ / A

R = ℓ / σA

Conductivity

σ = 1/ ρ

Light (photon) energy

E = hf

Photoelectric effect

hf = φ + ½mvmax2

EAT (Good Enough to Eat)

Stokes’ Law

F = 6πrvη

Refractive index

μ = sini / sinr = v1 / v2

SUR (Spare Part Surgery)

Stress (tensile or compressive)

σ = F / A

Strain (tensile or compressive)

ε = Δx / x

Elastic strain energy

ΔEel = FΔx / 2

Thin lens equation

1/v + 1/u = 1/f

 

SECOND-YEAR UNITS

TRA (Transport on Track)

Momentum

p = mv

Net force, where mass is constant

F = dp/dt

Force on a current-carrying wire in a magnetic field

F = BIℓ sin θ

Faraday’s and Lenz’ laws combined

E = −d(NΦ)/dt

Voltage in a transformer coil

Ns/Np = Vs/Vp

Capacitance

C = Q / V

Exponential discharge in a capacitor

Q = Q0e−t/RC

MDM (The Medium is the Message)

Attenuation in an optical fibre

I = I0e-μx

Capacitors (Quality Varies Considerably)

Q = VC

Energy stored in a capacitor

W = ½QV

W = ½CV2

Electric field strength (Feq)

E = F / Q

Electric field strength (Ved)

E = V / d

Force on a charged particle moving in a magnetic field

F = Bqv sin θ

PRO (Probing the Heart of Matter)

Mass-energy

ΔE = c2Δm

Electrostatic force

F = kQ1Q2 / r2

where k = 1 / 4πε0 (for the value of ε0, refer to the data table)

Strength of an electric field due to a point charge

E = kQ / r2

Kinetic energy of a particle

Ek = p2 / 2m

note that the particle must be travelling much slower than the speed of light

de Broglie wavelength of a particle

λ = h / p

Electronvolts

1 eV = 1.60 × 10−19 J

Kinetic energy of a charged particle accelerated by a p.d.

Ek = QV

Radians

π rad = 180°

2 π rad = 360°

1 radian = 180 / π degrees

1 degree = π / 180 radians

Angular velocity

v = ωr

T = 2π / ω

Centripetal force

F = mv2 / r

Centripetal acceleration

a = v2 / r

a = rω2

Radius of a charge particle’s path in a magnetic field

r = p / BQ

BLD (Build or Bust)

Speed of longitudinal waves in a solid

v = √(E / ρ)

Simple harmonic motion: condition required

F = −kx

Simple harmonic oscillators

a = −ω2x

a = −Aω2 cos ωt

T = 2π / ω

Total energy of an oscillating system

Etot = Ekin + Epot

STA (Reach for the Stars)

Luminous flux from a sphere

F = L / 4πd2

Rate of nuclear decay

dN/dt = −λN

Half-life

Decay constant

t1/2 = ln2 / λ

λ = ln2 / t1/2

Nuclear decay

N = N0e-λt

Nuclear binding energy

ΔE = c2Δm

Gravitational attraction force

F = Gm1m2 / r2

Strength of a gravitational field due to a point mass

g = GM / r2

Gas equation (Pervnert)

pV = nRT

Average kinetic energy of a gas molecule

½mác2ñ = 3kT / 2

Doppler shift of light

z = Δλ / λ ≈ Δf / f ≈ v/c

Redshift from stars

z = H0d / c

 

DATA

Acceleration of free fall

g

 9.81

m s-2

Molar gas constant

R

 8.31

J K-1 mol-1

Boltzmann constant

k

 1.38 × 10-23

J K-1

Permeability of free space

μ0

 4π × 10-7

N A-2

Electron charge

e

-1.60 × 10-19

C

Permittivity of free space

ε0

 8.85 × 10-12

F m-1

Electron mass

me

 9.11 × 10-31

kg

Planck constant

h

 6.63 × 10-34

J s

Electronvolt

1 eV

 1.60 × 10-19

J

Proton mass

mp

 1.67 × 10-27

kg

Gravitational constant

G

 6.67 × 10-11

N m2 kg-2

Speed of light in a vacuum

c

 3.00 × 108

m s-1

Gravitational field strength

g

 9.81

N kg-1

 

 

Physical quantities

Name

meaning

symbol

units

name of units

Magnetic flux density

The number of lines of magnetic flux per square metre

B

T

Wb m-2

tesla

weber per m2

Magnetic flux

The number of magnetic field lines (an idea I find difficult to understand properly)

Φ

Wb

weber

Focal length

The distance between a lens and the focal point, the point where all the rays of light passing through the lens converge (cross over)

f

m

metre

Ubject

The distance between a lens and the object it is focusing light from

u

m

metre

Vimage

The distance between a lens and the image it forms on a surface

v

m

metre

Resistivity

How much a given thickness (cross sectional area) of material resists electric current per unit length

ρ

Ωm

Ohm metre