A2 Physics Formulas

This isn’t finished yet but I hope to update it as the year goes on with all the good bits that are important in exams. If you want anything specific to be included here, email physics@benjamin-mills.com and Jim’ll Fix It as soon as possible.

Log-log graphs

To draw a log-log graph:

· find a power-law equation,

· turn each term into a logarithm,

· plot the log equation as a straight line graph

Imagine this – you’re in the exam and you get this question:

Plot a log-log graph of the equation y =Ax^p

To turn it into a log equation, rewrite each part as follows (powers become coefficients, variables and their coefficients become logs):

A real-life physics example of this technique is making a log-log graph of Coulomb’s law: F = (kQq)/r²

Coulomb’s law states that the electromagnetic force F between two charged spheres, of charges Q and q respectively, is equal to the product of the charges Q and q and the constant of proportionality k divided by the square of the distance, r, between the two charged spheres. In English that translates to: If you want to find the force separating two charged balls, multiply the both the charges together and times that by k (about 9 billion). Then divide the lot by the square of the distance between the balls.

To make life easier I’d convert it into the form y = Ax^p, which is F = kQqr^-2. Q, q and k are coefficients so they are represented as a whole by A. F is the dependent variable and as such is represented by y. r is the independent variable and is represented by x. Let’s look at the blackboard, children:

If I draw log(F) = -2log(r) + log(kQq) as a straight-line graph it looks like this:

Full list of A2 formulas

v=ωr	linear velocity = angular velocity x radius of orbit	ms^-1= rad.s^-1 m*
p=mv	momentum = mass x velocity	kgms^-1= kg ms^-1*
F=Δp/Δt	net force = change in momentum ÷ change in time	N or kgms^-2= kgms^-1÷ s
F=BIℓsinθ	force on a wire in a magnetic field = magnetic flux density x current in wire x length of wire x sin(angle between wire and magnetic field lines)	N = NA^-1m^-1 A * m*
Φ=BA	magnetic flux in a loop of wire = magnetic flux density x area enclosed by loop	NA^-1m = NA^-1m^-1 m²*
ℰ=-d(NΦ)/dt	electromotive force = instantaneous rate of change of flux linkage	V = NA^-1m ÷ s or kgm²s^-3A^-1 = kgm²s^-2A^-1 ÷ s
N_s/N_p=V_s/V_p	number of turns in primary coil of transformer ÷ number of turns in secondary coil = voltage in primary ÷ voltage in secondary	ratio → no units!
C=Q/V	capacitance of a capacitor = charge stored by it ÷ voltage across it	Farads, F = CV^-1 = C²/J
Q=Q₀e^-t/RC	charge in a capacitor at time-t = charge at time-zero x Euler’s number to the power (- time ÷ resistance x capacitance)	Coulombs, C
I=I₀e^-μx	intensity of light in an optical fibre at distance-x = intensity at distance-zero x Euler’s number ^ (- absorption coefficient of fibre x distance-x)	Wm^-2
W=½QV	Energy stored by a capacitor = 0.5 x charge stored x voltage across it	Joules, J = C JC^-1*
W=½CV²	Energy stored by a capacitor = 0.5 x capacitance squared x voltage across it	J = CV^-1V²=AsV*
E=V/d	Electric field strength = potential difference between two plates ÷ the distance between them	Vm^-1
E=F/Q	Electric field strength = force experienced per unit charge	NC^-1
F=Bqvsinθ	Force experienced by an electron in a wire = magnetic flux density x charge of particle x speed of particle x sin(angle between particle’s path and magnetic flux lines)	m
ΔE=c²Δm	Rehash of E=mc², meaning change in energy = change in mass x 9x10¹⁶	J = m²s^-2 kg*
F=kQq/r²	Force separating two charged spheres = k x charge on sphere Q x charge on sphere q / distance between them squared	N = N^-1m^-4C² C²*
k=1/(4πε₀)	constant k in (F=kQq/r²) = 1/(4π x permittivity of free space) ε₀ ≈ 8.854 x 10^-12 Fm^-1	N^-1m^-2C² = Fm^-1
E=kQ/r²	Electric field strength (at distance r from a point charge) = k x charge / distance squared	NC^-1 = N^-1m^-4C³
E_k=p²/2m	Kinetic energy of a particle = momentum squared / 2 mass*
λ=h/p	de Broglie wavelength = Planck constant / momentum
F=mv²/r	centripetal force = mass x linear velocity squared / radius of orbit
r = p/Bq	radius of orbit = momentum / magnetic field strength x charge
v=√(E/ρ)
F=-kx
a=-ω²x
a=-Aω²cosωt
x=Acosωt
T=2π/ω

Random knowledge

· The direction of an electric field is the direction a positive charge is forced in the field

· A polar molecule is rotated in a uniform electric field

· Baryons have 3 quarks and mesons have 2 quarks

· Charge, energy and momentum are always conserved in interactions between particles (e.g. collisions)

· High energies are needed to overcome strong forces holding subatomic particles together, and to produce very short wavelengths which are needed to see fine detail (by diffraction or transparency)

· MeV, GeV are energy and MeV/c² and GeV/c² are mass

· 1 radian = 180/π degrees ≈ 57.3°

· 1 degree = π/180 radians ≈ 0.0175 rad

Circular Motion

v = ωr

Velocity in a straight line is equal to angular velocity times radius

T = 2π/ω → ω = 2π/T

Time period is equal to circumference (in radians) divided by angular velocity

Angular velocity is equal to circumference (in radians) divided by time period

a = v²/r

Acceleration is equal to linear velocity squared divided by radius

a = rω²

Acceleration is equal to radius times angular velocity squared