Physics equations CIE iGCSE

density

density = mass / volume; ρ = m / V

average speed

average speed = distance / time; v = d / t

acceleration

acceleration = change in velocity / time; a = (v − u) / t

weight

weight = mass × gravitational field strength; W = mg

spring force

spring force = spring constant × extension; F = kx

resultant force

resultant force = mass × acceleration; F = ma

moment

moment = force × perpendicular distance to pivot

momentum

momentum = mass × velocity; p = mv

impulse

impulse = force × time = change in momentum; Ft = mv − mu

kinetic energy

kinetic energy = ½ × mass × speed²; Ek = ½mv²

gravitational potential energy change

change in gravitational potential energy = mass × g × change in height; ΔEp = mgΔh

work done

work done = force × distance moved in the direction of the force; W = Fd

power

power = energy / time; P = E / t

efficiency (energy)

efficiency = useful energy output / energy input × 100%

efficiency (power)

efficiency = useful power output / power input × 100%

pressure

pressure = force / area; p = F / A

pressure in a fluid

pressure in a fluid = density × gravity × depth; p = ρgh

Boyle’s law

Boyle’s law: p₁V₁ = p₂V₂

gas law

gas law: p₁V₁ / T₁ = p₂V₂ / T₂

thermal capacity

thermal capacity = mass × specific heat capacity; C = mc

change in thermal energy

change in energy = mass × specific heat capacity × temperature change; E = mcΔT

charge

charge = current × time; Q = It

potential difference (energy)

potential difference = energy / charge; V = E / Q

potential difference (Ohm’s law)

potential difference = current × resistance; V = IR

electrical power

electrical power = IV = I²R = V² / R

electrical energy

electrical energy = current × potential difference × time; E = IVt

resistance in series

total resistance in series = R₁ + R₂ + R₃

resistance in parallel

total resistance in parallel = 1/RT = 1/R₁ + 1/R₂ + 1/R₃

induced emf

induced e.m.f. ∝ rate of change of magnetic flux linkage

transformer equation

transformer equation: VP / VS = NP / NS

transformer power

power in a transformer: I_pV_p = I_sV_s

wave speed

wave speed = frequency × wavelength; v = fλ

frequency

frequency = 1 / period; f = 1 / T

Snell’s law

Snell’s law: n₁ sinθ₁ = n₂ sinθ₂

refractive index

refractive index = speed of light in vacuum / speed of light in medium; n = c / v

critical angle

sin(critical angle) = 1 / refractive index; sin c = 1 / n

speed of light

speed of light in vacuum = 3.0 × 10⁸ m/s

orbital speed

orbital speed = 2π × radius of orbit / period; v = 2πr / T

Hubble constant (definition)

Hubble constant = recession velocity / distance from Earth; H₀ = v / d

Hubble constant (value)

Hubble constant = 2.2 × 10⁻¹⁸ s⁻¹

age of universe

estimate of the age of the universe: t= d/v =1/H₀; age ≈ 1 / H₀