IM Syllabus (2013): Physics
Data and Formulae Booklet
The following equations may be useful in answering some of the questions in the examination.
Uniformly accelerated motion:
Circular motion:
v = u + at
1
s = ut + at 2
2
2
2
v = u + 2as
⎛u+v⎞
s=⎜
⎟t
⎝ 2 ⎠
Useful formulae:
F = kΔx
F
σ =
A
Δl
ε=
l
Hooke's law:
Stress:
Strain:
Young's modulus:
Y=
σ
ε
Energy stored in a stretched wire:
E=
1
2k
( Δl ) 2
Fields due to point sources:
Period:
T = 2π r
v
Momentum:
p=mv
Newton’s second law:
F = ma
Kinetic energy:
KE =
Gravitational potential energy:
PE = Δ ( mgh )
Mechanical work done:
W = FΔd
1
2 mv
2
Vibrations and waves:
Q1 Q2
Force between point charges:
F=
Force between point masses:
M M
F = G 12 2
r
4πε 0 r 2
Current electricity:
Acceleration in s.h.m.: a = –k x
Period:
T = 2π
Velocity of a wave:
v = fλ
k
Electromagnetism:
Current:
I = nAve
Ohm’s law:
V = IR
Resistors in series:
RTOTAL = R1 + R2 + …
Power:
a=
Mechanics:
Materials:
Resistors in parallel:
v2
r
Centripetal acceleration:
1
RTOTAL
=
E=
Electric field strength:
1
1
+
+ ...
R1 R 2
2
P = IV = I R = V
2
R
F
q
Electric potential (uniform field): V = E d
Energy of a particle accelerated by an electric field:
QV = Δ
(
1
2 mv
2
)
Force on a moving charge:
F = BQv
Magnetic flux:
Φ = BA
Force on current:
F = BIl
Emf induced in a moving conductor:
E = Blv
1
IM Syllabus (2013): Physics
Induced emf:
Charge on capacitor:
Q = CV
Parallel-plate capacitor:
C=
ε 0ε r A
d
Root mean square for sinusoidal alternating current
I
V
and voltage:
I rms = 0 ; V rms = 0
2
2
Physics of nuclei and atoms:
Ray optics:
Magnification:
dt
Alternating current:
Capacitance:
Thin lenses:
E = − N dΦ
1 1 1
= + (real is positive)
f
u v
1 1 1
= − (Cartesian)
f
v u
v h
m = = i (real is positive)
u ho
m=−
Radioactivity:
A = λN
Mass-energy relation:
E = mc 2
Line spectra:
ΔE = hf = hc
λ
h
v
= − i (Cartesian)
u
ho
Mathematical Formulae:
Surface area of a sphere:
S = 4π r 2
Volume of a sphere:
V=
Surface area of a cylinder:
S = 2π rh + 2π r 2
Volume of a cylinder:
V = π r 2h
4 3
πr
3
The following constants may be useful in answering some of the questions in the examination.
Acceleration of free fall on and near the Earth’s surface g = 9.81 m s−2
Gravitational field strength on and near the Earth’s surface g = 9.81 N kg−1
Coulomb’s law constant k = 1/(4πεo) = 8.99 × 109 N m2 C−2
Charge of an electron e = −1.60 × 10−19 C
Mass of an electron me = 9.11 × 10−31 kg
Electronvolt 1 eV = 1.60 × 10−19 J
Gravitational constant G = 6.67 × 10−11 N m2 kg−2
Permittivity of free space εo = 8.85 × 10−12 F m−1
Planck constant h = 6.63 × 10−34 J s
Speed of light in a vacuum c = 3.00 × 108 m s−1
Unified atomic mass unit u = 1.66 ×10−27 kg
2