DO PHYSICS ONLINE
EQUATION FORMULAE LIST
EQUATION MINDMAPS
Equations are essential part of physics, without them, we can’t start to explain our
physical world and make predictions. An equation tells a story – a collection of a
few symbols contains a wealth of information. Many examination questions can be
answered by having an in-depth understanding of equations. To help you maximize
your examination marks, you should use the equation mindmaps (templates) to gain
this in-depth understanding. You need to commit to memory much of the
information contained in the equation mindmaps so that you can appreciate the
story told by each equation.
The Formula Sheet provided in the exam is not ordered very well, many important
equations you should know are missing and the formatting and symbols used are not
always the clearest or best. The equations appearing in the Formula Sheet are shown
within the boxes. Other alternative forms and extra equations are shown without
boxes. It is best that all the equations given below are committed to memory. This will
make a big difference to your exam mark.
SPACE
vav 
v
dx
dt
aav 
a
r
t
v v  u

t
t
dv
dt
F  ma
a
F
m
F  mg
Average velocity
Instantaneous velocity in x-direction
Average acceleration
Instantaneous acceleration in x-direction
Newton’s Second Law
acceleration
Weight of an object
1
F m
v2
r
Centripetal force: uniform circular motion
F v2
ac  c 
m
r
Centripetal acceleration
g  force 
ag
g
g-force (g = +9.8 m.s-2)
g  force 
FAB   FBA
Newton’s Third Law
Frocket   Fgases
eg rocket propulsion
p  mv
Momentum of a moving object
impulse  F t
Impulse of a force F acting for a time interval t
J  F t  m v  m u
Impulse = change in momentum
F  0
 p  0 Law of Conservation of momentum
W Fs
EK  12 m v 2
W  F s  12 m v 2  12 m u 2
W  qV
1
2
apparent weight m a  m g

normal weight
mg
m v 2  eV
Work done by a force during a
displacement
Kinetic energy of a moving object
Work done = change in KE
Work done on a charge in an electric field
Gain in KE electron due to a constant
accelerating voltage
2
v  u  at
s  ut  at
1
2
Equation for uniform accelerated motion in onedimension
2
v2  u2  2 a s
a = constant
uv
vav 
2
s  vav t
vx 2  ux 2
Equations for Projectile Motion
v  u  at
v y 2  u y 2  2 a y y
x  ux t
y  u y t  12 a y t 2
ux  u cos 
motion in x-direction (horizontal)
+x direction is positive
ax  0
vx  ux
sx  ux t
u y  u sin 
vy  uy  ay t
s y  u y t  12 a y t 2
vy2  uy2  2 ay sy
motion in y-direction (vertical)
+y direction is positive (vertically up)
s  sx  s y
2
2
2
v 2  vx 2  v y 2
tan  s 
tan  v 
ay = - 9.8 m.s-1
sy
sx
vy
vx
3
F
G m1 m2
d2
F
G m1 m2
r2
g planet 
Gravitational force
G M planet
E p  G
R planet
Acceleration due to gravity at surface of a
planet
m1 m2
r
Gravitational potential energy
Gravitational potential energy near Earth’s
surface
Ep  m g h
g
G ME
G ME

2
2
r
 RE  h 
Acceleration due to gravity (Earth)
Period of pendulum  g
L
T  2
g
Kepler’s Third Law for satellite motion
r 3 GM

T 2 4 2
r13 r2 3

T12 T2 2
r13 r2 3

T12 T2 2
3
 r 2
T2  T1  2 
 r1 
vorb 
T
GM
r
2 r
vorb
vesc 
2GM
r
orbital velocity
orbital period
geostationary satellite T = 24 hours
escape velocity
4
E  mc 2
lv  l0 1 
tv 
Equations of Einstein’s Special Relativity
v2
c2
t0
v2
c2
m0
1
mv 
1
v2
c2
5
Motors and Generators
V
I
P V I
Energy  V I t
Resistance
F
II
k 1 2
l
d
Magnetic force between two parallel
conductors
F  B I L sin 
Magnetic force on a conductor
R
B
Electrical power
Electrical energy
0 I
2 r
Magnetic field surrounding a long straight
conductor
 Fd
  n B I A cos 
Torque
Torque on a coil in a magnetic field
 B  B A cos 
Magnetic flux
 
 B
t
average induced emf
 
dB
dt
induced emf
 B  B A cos  t     t
   B A sin  t 
electric motor: back emf  back
 battery  I R   back
Vp
Vs

Vs 
Transformer equation:
step up or step down voltages
np
ns
ns
Vp
np
Ps  Pp
Ploss  I 2 R
Is 
np
ns
Ip
Vs I s  V p I p
ideal transformer
Power loss (eddy currents – transformer,
induction heating; transmission lines)
6
From Ideas to Implementation
F  q v B sin 
E
F
q
E
V
d
Force on a charged particle moving in a
magnetic field
Electric field
Electric field (constant) between two parallel
charged plates
Eh f
Energy of a photon
c f 
Speed of light
Speed of electromagnetic radiation
1
2
m v 2  eV
Gain in KE of electron due to accelerating
voltage
Photoelectric Effect
h f  12 m v 2  W
h f  12 m vmax 2  Wmin
1
2
m vmax 2  h f  Wmin
eVs  12 m vmax 2
Vs 
Stopping voltage
h f Wmin

e
e
eVs  12 m vmax 2  0
h f c  Wmin
n   d sin 
Cut-off (critical) frequency
W
f c  min
h
Bragg’s Law – crystal structure (constructive
interference)
7
From Quanta to Quarks
 1
1 
 R 2  2 
n

ni 
 f
Hydrogen atom - spectrum
E2  E1  h f
Bohr Model of atom
1
h
2
L  mvr 
En  

n = 1, 2, 3, …
Energy levels hydrogen atom
r1  5.29  1011 m
Allowed orbits for electrons in
hydrogen atom
de Broglie wavelength
de Broglie relationship
h
mv
Eh f

E1  13.6 eV
E1
n2
rn  r1 n 2
Angular momentum quantized
h
p
x p 
c f 
p
h
4
h

p
h

Photon
Matter wave
Heisenberg Uncertainty Principle
8
m  M products  M reactants
Mass defect
E  m c2
Einstein – mass/energy
9
Be4  4 He2 12 C6 1 n0
Chadwick discovers
neutron
Beta plus decay
p+  n + e+ +  e
Beta decay
Pauli & Fermi neutrino
19Ne
10

19F
9
+ e+ + e
e+  +
p[d(-1/3) u(+2/3) u(+2/3)]
 n[d(-1/3) u(+2/3) d(-1/3)]
Beta minus decay
n  p   e   e
232
Th90 228 Ra 88  4 He2
4
Alpha decay
He2  
Standard model
proton
d (-1/2)
u (+2/3)
u (+2/3)
Proton
neutron
d (-1/3)
u (+2/3)
d (-2/3)
235U + 1n 
92
0
236U * 
92
136Xe + 88Sr
56
36
Neutron
matter wave
Nuclear fission
+ 121n0
9