Equations

Every equation in the AQA GCSE Physics specification. You must learn the ones marked “Must recall”; the others are given on the equation sheet in the exam.

4.1 Energy

Must recall
kinetic energy = 0.5 × mass × speed²
$E_k = \tfrac{1}{2} m v^2$
Symbol Meaning Unit
Eₖ kinetic energy J
m mass kg
v speed m/s
See the notes for 4.1.1
Must recall
gravitational potential energy = mass × gravitational field strength × height
$E_p = m g h$
Symbol Meaning Unit
Eₚ gravitational potential energy J
m mass kg
g gravitational field strength N/kg
h height m
See the notes for 4.1.1
Must recall
power = energy transferred ÷ time
$P = \frac{E}{t}$
Symbol Meaning Unit
P power W
E energy transferred J
t time s
See the notes for 4.1.1
Must recall
power = work done ÷ time
$P = \frac{W}{t}$
Symbol Meaning Unit
P power W
W work done J
t time s
See the notes for 4.1.1
Must recall
efficiency = useful output energy transfer ÷ total input energy transfer
$\text{efficiency} = \frac{\text{useful output energy transfer}}{\text{total input energy transfer}}$
Symbol Meaning Unit
efficiency a decimal or percentage -
See the notes for 4.1.2
Must recall
efficiency = useful power output ÷ total power input
$\text{efficiency} = \frac{\text{useful power output}}{\text{total power input}}$
Symbol Meaning Unit
efficiency a decimal or percentage -
See the notes for 4.1.2
Given on equation sheet
elastic potential energy = 0.5 × spring constant × extension²
$E_e = \tfrac{1}{2} k e^2$
Symbol Meaning Unit
Eₑ elastic potential energy J
k spring constant N/m
e extension m
See the notes for 4.1.1
Given on equation sheet
change in thermal energy = mass × specific heat capacity × temperature change
$\Delta E = m c \Delta \theta$
Symbol Meaning Unit
ΔE change in thermal energy J
m mass kg
c specific heat capacity J/kg°C
Δθ temperature change °C
See the notes for 4.1.1

Symbol	Meaning	Unit
Eₖ	kinetic energy	J
m	mass	kg
v	speed	m/s

Symbol	Meaning	Unit
Eₚ	gravitational potential energy	J
m	mass	kg
g	gravitational field strength	N/kg
h	height	m

Symbol	Meaning	Unit
P	power	W
E	energy transferred	J
t	time	s

Symbol	Meaning	Unit
P	power	W
W	work done	J
t	time	s

Symbol	Meaning	Unit
efficiency	a decimal or percentage	-

Symbol	Meaning	Unit
efficiency	a decimal or percentage	-

Symbol	Meaning	Unit
Eₑ	elastic potential energy	J
k	spring constant	N/m
e	extension	m

Symbol	Meaning	Unit
ΔE	change in thermal energy	J
m	mass	kg
c	specific heat capacity	J/kg°C
Δθ	temperature change	°C

4.2 Electricity

Must recall
charge flow = current × time
$Q = I t$
Symbol Meaning Unit
Q charge flow C
I current A
t time s
See the notes for 4.2.1
Must recall
potential difference = current × resistance
$V = I R$
Symbol Meaning Unit
V potential difference V
I current A
R resistance Ω
See the notes for 4.2.1
Must recall
power = potential difference × current
$P = V I$
Symbol Meaning Unit
P power W
V potential difference V
I current A
See the notes for 4.2.4
Must recall
power = current² × resistance
$P = I^2 R$
Symbol Meaning Unit
P power W
I current A
R resistance Ω
See the notes for 4.2.4
Must recall
energy transferred = power × time
$E = P t$
Symbol Meaning Unit
E energy transferred J
P power W
t time s
See the notes for 4.2.4
Must recall
energy transferred = charge flow × potential difference
$E = Q V$
Symbol Meaning Unit
E energy transferred J
Q charge flow C
V potential difference V
See the notes for 4.2.4

Symbol	Meaning	Unit
Q	charge flow	C
I	current	A
t	time	s

Symbol	Meaning	Unit
V	potential difference	V
I	current	A
R	resistance	Ω

Symbol	Meaning	Unit
P	power	W
V	potential difference	V
I	current	A

Symbol	Meaning	Unit
P	power	W
I	current	A
R	resistance	Ω

Symbol	Meaning	Unit
E	energy transferred	J
P	power	W
t	time	s

Symbol	Meaning	Unit
E	energy transferred	J
Q	charge flow	C
V	potential difference	V

4.3 Particle model of matter

Must recall
density = mass ÷ volume
$\rho = \frac{m}{V}$
Symbol Meaning Unit
ρ density kg/m³
m mass kg
V volume m³
See the notes for 4.3.1
Given on equation sheet
thermal energy for a change of state = mass × specific latent heat
$E = m L$
Symbol Meaning Unit
E thermal energy for a change of state J
m mass kg
L specific latent heat J/kg
See the notes for 4.3.2
Given on equation sheetPhysics only
for a fixed mass of gas at constant temperature: pressure × volume = constant
$p V = \text{constant}$
Symbol Meaning Unit
p pressure Pa
V volume m³
See the notes for 4.3.3

Symbol	Meaning	Unit
ρ	density	kg/m³
m	mass	kg
V	volume	m³

Symbol	Meaning	Unit
E	thermal energy for a change of state	J
m	mass	kg
L	specific latent heat	J/kg

Symbol	Meaning	Unit
p	pressure	Pa
V	volume	m³

4.5 Forces

Must recall
weight = mass × gravitational field strength
$W = m g$
Symbol Meaning Unit
W weight N
m mass kg
g gravitational field strength N/kg
See the notes for 4.5.1
Must recall
work done = force × distance (along the line of action of the force)
$W = F s$
Symbol Meaning Unit
W work done J
F force N
s distance m
See the notes for 4.5.2
Must recall
force applied to a spring = spring constant × extension
$F = k e$
Symbol Meaning Unit
F force N
k spring constant N/m
e extension m
See the notes for 4.5.3
Must recallPhysics only
moment of a force = force × distance (normal to direction of force)
$M = F d$
Symbol Meaning Unit
M moment of a force Nm
F force N
d perpendicular distance from the pivot m
See the notes for 4.5.4
Must recallPhysics only
pressure = force normal to a surface ÷ area of that surface
$p = \frac{F}{A}$
Symbol Meaning Unit
p pressure Pa
F force normal to the surface N
A area m²
See the notes for 4.5.5
Must recall
distance travelled = speed × time
$s = v t$
Symbol Meaning Unit
s distance m
v speed m/s
t time s
See the notes for 4.5.6
Must recall
acceleration = change in velocity ÷ time taken
$a = \frac{\Delta v}{t}$
Symbol Meaning Unit
a acceleration m/s²
Δv change in velocity m/s
t time s
See the notes for 4.5.6
Must recall
resultant force = mass × acceleration
$F = m a$
Symbol Meaning Unit
F resultant force N
m mass kg
a acceleration m/s²
See the notes for 4.5.6
Must recallHT only
momentum = mass × velocity
$p = m v$
Symbol Meaning Unit
p momentum kg m/s
m mass kg
v velocity m/s
See the notes for 4.5.7
Given on equation sheetHT onlyPhysics only
pressure due to a column of liquid = height of column × density of liquid × gravitational field strength
$p = h \rho g$
Symbol Meaning Unit
p pressure Pa
h height of the column m
ρ density of the liquid kg/m³
g gravitational field strength N/kg
See the notes for 4.5.5
Given on equation sheet
(final velocity)² − (initial velocity)² = 2 × acceleration × distance
$v^2 - u^2 = 2 a s$
Symbol Meaning Unit
v final velocity m/s
u initial velocity m/s
a acceleration m/s²
s distance m
See the notes for 4.5.6
Given on equation sheetHT onlyPhysics only
force = change in momentum ÷ time taken
$F = \frac{m \Delta v}{\Delta t}$
Symbol Meaning Unit
F force N
mΔv change in momentum kg m/s
Δt time taken s
See the notes for 4.5.7

Symbol	Meaning	Unit
W	weight	N
m	mass	kg
g	gravitational field strength	N/kg

Symbol	Meaning	Unit
W	work done	J
F	force	N
s	distance	m

Symbol	Meaning	Unit
F	force	N
k	spring constant	N/m
e	extension	m

Symbol	Meaning	Unit
M	moment of a force	Nm
F	force	N
d	perpendicular distance from the pivot	m

Symbol	Meaning	Unit
p	pressure	Pa
F	force normal to the surface	N
A	area	m²

Symbol	Meaning	Unit
s	distance	m
v	speed	m/s
t	time	s

Symbol	Meaning	Unit
a	acceleration	m/s²
Δv	change in velocity	m/s
t	time	s

Symbol	Meaning	Unit
F	resultant force	N
m	mass	kg
a	acceleration	m/s²

Symbol	Meaning	Unit
p	momentum	kg m/s
m	mass	kg
v	velocity	m/s

Symbol	Meaning	Unit
p	pressure	Pa
h	height of the column	m
ρ	density of the liquid	kg/m³
g	gravitational field strength	N/kg

Symbol	Meaning	Unit
v	final velocity	m/s
u	initial velocity	m/s
a	acceleration	m/s²
s	distance	m

Symbol	Meaning	Unit
F	force	N
mΔv	change in momentum	kg m/s
Δt	time taken	s

4.6 Waves

Must recall
wave speed = frequency × wavelength
$v = f \lambda$
Symbol Meaning Unit
v wave speed m/s
f frequency Hz
λ wavelength m
See the notes for 4.6.1
Given on equation sheet
period = 1 ÷ frequency
$T = \frac{1}{f}$
Symbol Meaning Unit
T period s
f frequency Hz
See the notes for 4.6.1
Given on equation sheetPhysics only
magnification = image height ÷ object height
$\text{magnification} = \frac{\text{image height}}{\text{object height}}$
Symbol Meaning Unit
magnification a ratio (no unit) -
See the notes for 4.6.2

Symbol	Meaning	Unit
v	wave speed	m/s
f	frequency	Hz
λ	wavelength	m

Symbol	Meaning	Unit
T	period	s
f	frequency	Hz

Symbol	Meaning	Unit
magnification	a ratio (no unit)	-

4.7 Magnetism and electromagnetism

Given on equation sheetHT only
force on a conductor at right angles to a magnetic field carrying a current = magnetic flux density × current × length
$F = B I l$
Symbol Meaning Unit
F force N
B magnetic flux density T
I current A
l length of conductor in the field m
See the notes for 4.7.2
Given on equation sheetHT onlyPhysics only
p.d. across primary coil ÷ p.d. across secondary coil = turns on primary coil ÷ turns on secondary coil
$\frac{V_p}{V_s} = \frac{n_p}{n_s}$
Symbol Meaning Unit
Vₚ, Vₛ potential difference across the primary and secondary coils V
nₚ, nₛ number of turns on the primary and secondary coils -
See the notes for 4.7.3
Given on equation sheetHT onlyPhysics only
p.d. across primary coil × current in primary coil = p.d. across secondary coil × current in secondary coil
$V_p I_p = V_s I_s$
Symbol Meaning Unit
Vₚ, Vₛ potential difference across the primary and secondary coils V
Iₚ, Iₛ current in the primary and secondary coils A
See the notes for 4.7.3

Symbol	Meaning	Unit
F	force	N
B	magnetic flux density	T
I	current	A
l	length of conductor in the field	m

Symbol	Meaning	Unit
Vₚ, Vₛ	potential difference across the primary and secondary coils	V
nₚ, nₛ	number of turns on the primary and secondary coils	-

Symbol	Meaning	Unit
Vₚ, Vₛ	potential difference across the primary and secondary coils	V
Iₚ, Iₛ	current in the primary and secondary coils	A