Some of the concepts might be out of syllabus but I believe most of it is still relevant. It is a very concise summary containing mostly formulas and the Laws that govern Physics. This was done by a Raffles Institution student. I hope you will find this beneficial!

1. Homogenous: Units of both sides of
equation balances out.
YbXaQ  
Y
Y
n
X
X
m
Q
Q 
 nm
YXQ 
bYaXQ 
Absolute error is in 1 sf
Qty is in same dp as absolute error
Q
Q
%100

Q
Q
Fractional Error
% Error
Systematic Error: Results that differ from the true
values by a fixed amount.
Random Error: Results that scatter around a mean
value.
Precision: Agreement with each other.
Accuracy: Closeness with actual value.
2
2
1
2
1
22
)(
2
atuts
tvus
asuv
atuv




2
vF
vF
d
d


Thermal Equilibrium: Rate of heat gain = Rate of heat loss No net
flow of heat
0th
law: If A and B are separately in thermal eqm with C, then A and B
are in thermal eqm with each other.
1st
law: Internal Energy of a system is dependant only on its state. An
increase in the U of a system is the sum of work done on the
system and the heat supplied to the system.
WQU 
Internal Energy: The sum of all microscopic KE
and PE of molecules in the object.
Temperature: A measure of the average KE.
VpWxFW 
Isothermal: No ∆T;
Isovolumetric: No ∆V
Isobaric: No ∆p
Adiabatic: No ∆Q; switches between isotherms
VpnRTpV 1
2
2
1
2
3
2
3
1
cmkT
cNmpV
NkTpV



Mean KE of molecule
1st
law: A body continues its state of rest of motion or rest unless a
resultant external force acts on it [Inertia].
2nd
law: Rate of change of momentum is proportional to resultant force
and acts in the direction of the force [F=ma].
3rd
law: If body A exerts a force on body B, then body B exerts an equal
but opposite force on body A [action-reaction pair].
Inertia: A body’s reluctance to change its state of
rest/motion.
Mass: A measure of a body’s inertia.
ma
dt
mvd
F 
)(
mvp 
pFt Impulse
Law of Conservation of Linear Momentum:
When bodies in a system interact, the total
momentum remains constant, provided no net
external force acts on the system.
22112211 vmvmumum


1221 vvuu For elastic collisions,
where k is Boltzmann constant
Effective weight:
Total force tt obj exerts on a spring
scale.
a
W
S
Where W = weight
W’ = effective weight
S = W’ (action-reaction)
S – W = ma
Absolute Zero: Minimum Internal Energy at 0K.
Specific Heat Capacity: The qty of heat required to raise the
temperature of 1kg of the material by
1K.
Specific Latent Heat of Fusion: The heat energy required to
change the state of 1kg of the
material from solid to liquid
without a change in
temperature.

2. cosFsW Scalar qty
Energy: The capacity to do work.
KE: E possessed by virtue of its motion.
PE: E possessed by virtue of its position.
2
2
12
2
1 mumvW 
Work-Energy
Theorem
Fv
dt
Fsd
P 
)(




2



T
rv
rs
2
2
2
2 2
r
Mm
G
T
mr
r
Mm
Gmr 








3
2
2 4
r
GM
T

Kepler’s
Third Law
r
GMm
U GPE
Escape Velocity => GPE + KE ≥ 0
Hooke’s Law: The extension of a spring is proportional to
the load if the limit of proportionality is not exceeded.
2
2
1
2
1 kxWFxWkxF 
F
x
F1
F2
x2x10
))((
))((
)(
12122
1
12122
1
2
122
1
2
12
12
22
1
FFxx
xxxxk
xxk
kxkx



Work Done
in extending
spring
Fl
hgp
A
F
p


A
Ahg)(  
mg
gV
hgA

 
Resultant
Upthrust
.: Upthrust = weight of fluid displaced
.: Resultant force = W - U
W
N
mg
r
mv
r
mv
WN


2
2
If , water will stay in bucket
0
2
 W
r
mv
N
Rate of ∆ of
angular
displacement
r
v
v
t
v
t
v
a
2




 

where r = radius of circular motion
M=center of mass of circular motion
2
2
1
2
2
21
)( tgh
dr
d
r
GM
g
r
mm
GF



Gravitational Field Strength:
Gravitational force per unit
mass
r
GM

Geostationary satellite:
Rotates at the same angular velocity as
the Earth, located above the Equator
Gravitational Potential:
The work done per unit mass by an external agent in
bringing a small mass from infinity to that point.
Since PE at ∞ is zero, and work is done by
gravity to bring an object from ∞ to a pt,
hence, GPE is negative [still scalar]
Couple: Pair of equal and opposite parallel forces
whose line of action do not coincide.
Translation Eqm: Resultant force is zero.
Rotational Eqm: Resultant torque about any axis
is zero.
Centripetal force:
A force that acts perpendicular to
the direction of motion and
directed towards the center of the
circular path.

3. e
x
 
22
2
1
22
0
2
2
1
2
max2
1
xmE
xxmE
mvE
p
k





m
k
axax
m
k
makx
makxkemg
maxekmg





2
2
)(







2


x
fv
2
2
4
kAI
r
P
Area
P
I



where A is amplitude
Transverse: Particles of the medium move in a direction
perpendicular to the direction of wave travel.
Longitudinal: “ “ parallel ” ”
A series of high and low pressure regions called
compressions and rarefactions.
EM waves:
oscillating electric and magnetic fields which are
perpendicular to each other and the dir of wave
propagation.
Polarised: particles vibrate in the same plane.
Stationary wave: Amplitude same.
Frequency same.
Wavelength same.
Direction different.
Radio waves >0.1m
Microwaves 0.1m – 0.1mm
Infra-red 0.1mm - 700nm
Visible light 700nm – 400nm
UV 400nm – 1nm
X-rays 1nm – 10pm
Gamma rays <10pm
wavelength
Amplitude
f
0x
0x
0x
x
v
0x
22
0 xxv  
Energy
Total Energy
KE
PE
displacement 0x
0
0
KE
PE
Total
t
No
Damping
Resonance
Light: Oscillation decays exponentially.
Critical: Returns to equilibrium v.quickly.
Heavy: No oscillation; returns to
equilibrium v.slowly.
Displacement
t
 
 
0max
0
0
cos
sin
xV
txx
txx






0
0
2
x
0
2
x
xa 2

x
a
SHM is the motion of a body, whose
acceleration directly proportional to
displacement and directed towards a fixed
point.
The negative sign shows tt a and x are
always opposite and directed towards
equilibrium.
E

4. L
Diffraction: Bending of waves around the sides of an
aperture. (aperture size should be
comparable to wavelength of wave)
Interference:
Superposition of coherent waves from identical
sources to form an observable pattern.
>Same amplitude
>Polarised in the same plane
>Coherent (in phase/constant phase diff)


nd
a
D
x
n 

sin
d
V
E
dr
dV
E
r
Q
V
VqU
r
Q
q
F
E
r
QQ
F







0
2
0
2
0
21
4
4
4



Electric field strength:
Force per unit charge acting on a
small positive charge placed at that
point.
Electric Potential:
Work done by external force in
moving a unit positive charge from
infinity to the point.
q can be –ve or +ve
∆V = Vfinal - Vinitial
A
l
R
I
V
R
Q
W
V
ItQ



 Current: Rate of flow of charge.
Charge: A fundamental property of matter
tt is –ve or +ve and gives rise to E force.
Coulomb: Qty of charge that passes a pt in
a circuit in 1s when there is 1A.
Pd: Amt of E energy converted to other
forms when a unit charge passes from one
pt to another. [EMF is reverse]
Volt: Pd between 2pts in which 1J is
converted when 1C passes thru.
Resistance: Ratio of the pd to the current.
Ohm: Resistance of a conductor in which
1A passes thru when pd is 1V.
Principle of SuperPosition:
When 2 or more waves arrive at the same pt at the same
time, the resultant displacement is equal to the vector
sum of the individual displacements due to each wave.
Wave is confined in a given space; no propagation of
energy.
Fundamental Mode = 1st
Harmonic [c=v/2L]
Overtone = 2nd
++ harmonic
Stationary waves are formed for which
wavelength:string length = a simple ratio (eg. 3:1)
Young’s
double slit
Diffraction
Grating
L4 L2c c c
End Correction:
Air molecules are slightly attracted to pipe material,
thus antinode is located slightly beyond the open end.
-+
e-
V V V
RI
R
V
IVP
2
2



Max Power when
external R = internal R.
V
RR
R
V 







21
1
0 0 0
Ohmic DiodeFilament
I I I
Where x is fringe width; dist
between adjacent bright/dark
fringes

5. Fleming’s LEFT HAND to
predict magnetic force.
Fleming’s RIGHT HAND to
predict induced Emf.
B
E
vQEBQv
m
QV
vQVmv




22
2
1
Acceleration thru
an electric field
Velocity Selector
where E is E-field
strength NOT Emf.
sinNBA
Faraday’s Law
Lenz’s Law:
The induced current always flows in a direction
to oppose the change that produces it.
dt
d
E


tNBA
dt
d
NBA
dt
d
E


cos
sin



[AC Generator]
Irms:
The value of the steady current which would dissipate heat at the
same rate in a given resistance as the AC.tVV
tII


sin
sin
0
0

 2
IIrms 
I
t0
I0
-I0
I0
2
I0
2
/2
RI
P
P
V
V
I
I
rms
rmsrms
2
000
222


When AC flows thru é primary, it sets up a varying
mag field in é core which links é primary to
secondary. With Faraday’s, é varying mag field
induces AC EMF across the wire in é secondary.
p
s
s
p
p
s
N
N
I
I
V
V
 cablecablesacrosslost R
V
P
P
2







Rectification:
Process of changing AC to DC.
nIB
nIB
r
NI
B
r
I
B
02
1
0
0
0
2
2









Flux density from an
infinitely long wire
At the centre of a circular
wire
Inside of a solenoid
At the end of a solenoid
Unit is
Tesla
The product of the area and magnetic flux
density that passes through it perpendicularly.
Weber (Wb)


sin
sin
BQvF
BIlF





sin
)sin(
)sin(
Blv
dt
Blsd
dt
BAd
E



[Moving Rod]







sin
sin
2
sin
sin
2
sin
2
2
1
2
2
1
BAf
T
Br
Br
r
Br
BlvE

















[Rotating Disc]
r
2
r
For sinusoidal only:
Heating effect of
current
Wires of low resistance
Heating effect of eddy
currents
Laminated iron core, cutting
across eddy currents
Heat loss from
magnetizing / reversing
the magnetic poles
Soft, easily magnetized iron

6. intensity
I
f
Vs
0
0 V
I
0-Vs



h
p
eV
KEhf
hfE
eVmv
s
s





max
2
max2
1
RelativeIntensity
Wavelength
X-rays are produced when the incident e-
had been accelerated by a high
voltage.
Not all e-
are stopped in a single collision => Continuous broad spectrum
Sharp intense lines when e-
are knocked out of the n=1 shell.
K-alpha for n=2 to n=1.
K-beta for n=3 to n=1.
Ka
Kb

2
k The more localized the wave packet (λ), the
larger the range of wavelengths (k) needed.
∆x small
∆k large
∆x large
∆k small
2
1



p
xkx
x
ψ
exponentially
decreasing
regionsinusoidal
U
2
2






tE
x
h
p
px


1
)(2
),2exp( 

 TR
EUm
kkLT

Obj A
Obj B
Work function is the
min energy to liberate
an e-
from its surface
Non-zero amplitude
indicates probable
transmission
Emission Spectra:
Gas is heated/bombarded with e-
. e-
are excited,
before emitting a photon. Diffraction Grating is
used to study line spectra.
Absorption Spectra:
When white light passes through cool gas, characteristic
frequencies of photons are absorbed. When these excited
atoms return to a lower state, the emitted photons are
scattered in all directions.
.:Dark lines.
L
A microscope is limited in its resolution by the
wavelength of the waves used for the image.
An electron microscope is limited by the low
wavelength, high momentum of Debroglie
.: pentration of the material surface.
STM’s limitation is the conductivity of the sample.
Heisenburg’s uncertainty principle
Uncertainty in e-
momentum is as large as
momentum of incoming photon
Smallest dist that produces separate image
Energy-time uncertainty
Photoelectric emission is the
emission of e-
from a metal
surface when exposed to EM
waves of sufficiently high
frequency.
Maxwellian model:
There should be measurable time lag between emission and
irradiation.
The max KE of photoelectron should depend on intensity, not
frequency.
Photoelectric emission should occur for all wavelengths since
energy is transmitted in a continuous manner.

7. Laser (read the notes)
Coherent: In phase
Collimated: Same dir
Monochromatic: 1 wavelength
Isotopes: Nuclei that have the same proton number but different number
of neutrons.
u: atomic mass unit; 1/12th
of the mass of a 12
C atom.
Mass Defect ∆m: The difference between the sum of the masses of the
nucleon and the mass of the actual nucleus.
AnH
eAnp
nucleusnp
mNmZm
ZmmNmZm
mNmZmm



)()(
)(
  2
cmBE 
Fe
U
H
Mass no, A
BEpernucleon
Fusion Fission
Coulomb repulsion > nuclear force
Conservation of
 Charge
 Momentum
 Mass-Energy
 Mass number
Radioactivity is the random and
spontaneous decay of an unstable nucleus
to a more stable one by emission of
particles and/or radiation.
Random: Don’t know which and
when a nucleus will decay
Spontaneous: Not affected by other
environmental factors
Background radiation is systematic
error.
α
particles
 Helium-4 nuclei
 High Ionising Power
 Air range of 3 - 4cm
 Stopped by paper
 Low hazard unless ingested
β  Moderate Ionising Power
 High speeds (0.5c)
 Stopped by 5mm of Al
 Stopped by surface tissues
γ  Produced when excited nuclei
returns to ground state
 Weak Ionising Power
 Stopped by few cm of lead
 Main radiation hazard due to
deep penetration
 Cancer, leukemia, cataracts,
hereditary defects
 Store in lead containers when not in use.
 Handle with a pair of tongs.
n
t
t
N
N
t
eAN
dt
dN
A
eNN
N
dt
dN













2
1
2ln
0
0
0
2
1





Decay Constant λ is the probability of decay of a nucleus per unit
time.
Where N is the no. of undecayed nuclei.
Activity A, is the rate of decay. (Bq)
Where A0 is the activity at t = 0.
Half-life is the time it takes for half of
a given no. of nuclei to decay.
Where n is the number of half-lives.
Constant
half-life
t
N