GCSE Physics Equations

physics_equations.md

Physics GCSE equations

AQA spec here

Energy and Particle Model of Matter

Changes in energy

Word equation	Symbol equation
kinetic energy = 1/2 x mass x (speed)2	Ek = 1/2mv2
elastic potential energy = 1/2 x spring constant x (extension)2	Ee = 1/2ke2
gravitational potential energy = mass x gravitational field strength x height	Ep = mgh

Specific Heat Capacity and Specific Latent Heat

Word equation	Symbol equation
change in thermal energy = mass x specific heat capacity x temperature change	∆E = mc∆T
energy for a change of state = mass x specific latent heat	E = mL

Energy is measured in Joules, J. Mass, m, in kg. SHC, c, in J/kg°C. Temperature change, ∆T, in °C. SLH, L, J/kg.

Power and work done

Work done is a measure of energy transfer when a force moves an object through a distance. They are both measured in Joules, J. Therefore:

P = E/t or P = W/t

where power (P) is measured in W and time (t) is measured in seconds.

Efficiency

efficiency = useful output energy transfer/useful input energy transfer

Efficiency may also be calculated as:

efficiency = useful power output/useful power input

Density and Pressure

Word equation	Symbol equation	Explanation
density = mass/volume	ρ = m/V	If m in kg and V in m3, then ρ in kg/m3
pressure x volume = constant	pV = constant	Pressure, p, in pascals, Pa. Volume, V, in cubic metres, m3

Electricity

Formula	Original Equation	Rearranged for..
		Potential Difference (V) / Volts, V	Current (I) / Amps, A	Resistance (R) / Ohms, Ω	Charge flow (Q) / Coulombs, C	Time (t) / Seconds, s	Power (P) / Watts, W	Energy (E) / Joules, J
Ohm's Law	V = IR	V = IR	I = V/R	R = V/I
General Charge Equation	Q = It		I = Q/t		Q = It	t = Q/I
Power Equation	P = IV	V = P/I	I = P/V				P = IV
Energy Equations	E = QV	V = E/Q			Q = E/V			E = QV
	E = Pt					t = E/P	P = E/t	E = Pt
---	---	---	---	---	---	---	---	---
Power + Ohm's Law	P = I^2R		I = √(P/R)	R = P/(I^2)			P = I^2R
	P = (V^2)/R	V = √(PR)		R = (V^2)/P			P = (V^2)/R
Energy + Charge	E = ItV	V = E/(It)	I = E/(tV)			t = E/(IV)		E = ItV

Resistance

Series

Rtotal = R1 + R2 + R3 ... Rn

Parallel

1/Rtotal = 1/R1 + 1/R2 + 1/R3 ... 1/Rn

Forces

Gravity

weight = mass × gravitational field strength

W = mg

Work done

work done = force x distance

W = Fs

Elasticity

force = spring constant × extension

F = ke

Force in newtons, N. Spring constant in newtons per metre, N/m. Extension in metres, m.

Forces and motion

Word equation	Symbol equation	Explanation
distance travelled = speed x time	s = vt
acceleration = change in velocity/time taken	a = ∆v/t
(final velocity)2 - (initial velocity)2 = 2 x acceleration x distance	v2 - u2 = 2as
resultant force - mass x acceleration	F = ma	Newton's second law

Moments, levers, gears

M = Fd

• Moment of a force, M, in Nm
• Force, F, in N
• Perpendicular distance, d, from pivot to the line of action of the force, in m.

If an object is balanced, the total clockwise moment about a pivot equals the total anti-clockwise moment about that pivot.

Momentum

p = mv

• Momentum, p, measured in kilograms metre per second, kgm/s or kgms^-1

In a closed system, the total momentum before an event is equal to the total momentum after the event. This is known as conservation of momentum.

When a force acts on an object that is moving, or able to move, a change in momentum occurs.

∆p = m∆v

The impulse on an object is equal to its change in momentum. Therefore:

I = ∆p

It is also true that

I = Ft

Because of this, impulse is measured in Ns (Newton seconds).

F (N) = m (kg) x a (ms-2)	I (Ns) = F (N) x t (s)
1N is described as 1kgms-2	1N x 1s must therefore be equal to 1kgms-1

As you can see, 1Ns = 1kgms^-1. Therefore, the units can be used interchangeably. However, it is standard practice to use Ns when describing an impulse.

Waves

Properties of waves

Word equation	Symbol equation	Explanation
wave speed = frequency x wavelength	v = fλ	Wave equation
period = 1/frequency	T = 1/f	Frequency in Hz

Lenses

magnification = image height/object height