Exam Cheat Sheet
Equation Sheet
CH 1, Circular Motion
Angular Displacement
s
θ =
r
Conversion between degrees and radians
to convert from degrees to radians, multiply by 2π/360°.
to convert from radians to degrees, multiply by 360°/2π.
Angular Speed
Δθ
ω =
Δt
- Angular Speed of one revolution
2π
ω =
T
Velocity in relation to angular speed (and radius/distance)
v = ωr
Centripetal acceleration
a = vω
2
v
2
a =
r
a = rω
2
Centripetal Force
mv
2
F =
= mrω
2
r
CH 2, Gravitational Force
G = 6.67×10
−11
2
N m kg
−2
, Universal Gravitational Constant
Newton's Law of Gravitation
F =
Gm 1 m 2
r
2
Gravitational Field Strength
GM
g =
r
2
Gravitational Potential Energy
GM m
g. p. e = −
r
Gravitational Potential
GM
φ = −
r
Gravitational Potential Difference
1
Δφ = GM (
1
−
r1
Velocity of Object to stay in circular orbit
v
2
GM
=
r
)
r2
Orbital Period
T
2
4π
2
= (
)r
3
GM
CH 3, Oscillations
Frequency-Period equation
1
f =
T
1
T =
f
Frequency and Angular Frequency
ω = 2πf
2π
ω =
T
Relationship between the displacement x and the time t
x = x 0 sin ωt
x = x 0 cos ωt
Acceleration in S.H.M
a = −a 0 cos ωt
2
a = −ω x
Velocity of an oscillator
v = v 0 cos ωt
v = ω√ (x
2
0
Maximum velocity of an oscillator
v 0 = ωx 0
Kinetic energy of an oscillator
1
2
− x )
1
E0 =
2
m(v 0 )
2
1
E0 =
2
m(ωx 0 )
2
CH 4, Thermal Physics
Internal energy of a system
ΔU = q + W
Work done by a volume of gas (at constant pressure)
W = pΔV
To convert between Celsius and Kelvin
θ(°C) = T (K) − 273.15
T (K) = θ(°C) + 273.15
Specific Heat Capacity
E
c =
mΔθ
Specific Latent Heat
E
L =
m
CH 5, Ideal Gases
k = 1.38×10
−23
R = 8.31 J K
J K
−1
N A = 6.02×10
23
mol
−1
−1
mol
, Boltzmann constant
, Molar Gas constant
−1
, Avogadro constant
Boyle's Law
P1 V1 = P2 V2
Ideal Gas Equation
V
RT
pV = nRT
pV = N kT
Pressure of an Ideal Gas
1
pV =
Nm < c
2
>
3
Deriving the equation:
change in momentum = −mc − (+mc) = −mc − mc = −2mc
2l
time between collisions with side ABCD =
c
2mc
f orce =
mc
2
=
2l
l
c
mc
2
mc
l
P ressure =
l
=
2
l
Nm < c
p =
l
2
2
3
>
3
1 Nm < c
p =
3
l
2
>
3
1 Nm < c
2
>
p =
3
V
Mean Translational Kinetic Energy of Atom ∝ T
Boltzmann Constant, k
R
k =
NA
Linking k.e with temperature
1
kinetic energy
=
m < c
2
2
CH 6, Uniform Electric Fields
kT
2
Root-Mean-Square Speed
c r.m.s = √ < c
3
>=
2
>
E =
electric field strength
Electric field strength
F
E =
Q
Strength of a electric field between two parallel metal plates
ΔV
E =
Δd
CH7, Coulomb's Law
ϵ 0 = 8.85×10
k =
1
4πϵ 0
−12
Fm
= 8.99×10
9
−1
, Permittivity of Free Space
mF
−1
Coulomb's Law
F =
kQ 1 Q 2
r
F =
2
Q1 Q2
4πε 0 r
2
The electric field strength due to a charge Q at a distance of r from its centre
Q
E =
4πε 0 r
2
kQ
E =
r
2
Work done for positive charge Q in moving it from a negative to a positive
plate
W
V =
Q
E = QV
E, W =
energy / work
Electrical potential V at a distance r from a charge Q
Q
V =
4πε 0 r
kQ
V =
r
Potential Energy of a pair of Point Charges(Electrical potential of moving
charge Q to charge Q from infinity)
1
2
Ep =
Q2 Q1
4πε 0 r
Electric Potential Difference
Q
1
ΔV =
1
(
4πε 0
−
r1
)
r2
CH8, Capacitance
Capacitance
Q
C =
V
Energy stored in a capacitor
1
W =
1
QV =
2
CV
2
1 Q
2
=
2
2
C
Capacitors in Parallel
C T = C 1 + C 2 +. . .
Capacitors in Series
1
1
=
CT
1
+
C1
+. . .
C2
Time constant for circuits containing capacitance and resistance
τ = CR
Discharge current graph, charge stored and potential difference across a
capacitor.
x = x0 e
(−
t
RC
)
CH9, Magnetic Fields and Electromagnetism
Magnetic Flux Density
B = F /I L
Force on a current-carrying conductor
F = BI Lsinθ
CH10, Motion of Charged Particles
Magnetic force on a moving charged particle (at right angles to a magnetic
field)
F = BQv
Magnetic force on a moving charged particle at angle θ to a magnetic field
F = BQv sin θ
Charge-to-Mass Ratio
e
=
me
2V ca
2
r B
e
v
=
me
Br
Velocity Selection equation
E
v =
B
The Hall voltage
BI
2
BI
VH =
ntq
CH11, Electromagnetic Induction
Magnetic Flux
Φ = BA
Φ = BA cos θ
Magnetic Flux Linkage
= BAN
= BAN cos θ
Magnitude of Induced E.M.F
ΔN Φ
E =
Δt
Lenz's Law
ΔN Φ
E = −
Δt
CH12, Alternating Current
Current on a sinusoidal graph at a given time
I = I 0 sin ωt
Voltage on a sinusoidal graph at a given time
V = V 0 sin ωt
Root-Mean-Square of voltage and current
V r.m.s =
V0
√2
I r.m.s =
I0
√2
Calculating power with r.m.s values
P = I
V
2
r.m.s
R = I r.m.s V r.m.s =
2
r.m.s
R
Deriving the Root-Mean-Square
< I
2
1
>=
2
I r.m.s = √ < I
2
2
I0
> = √
1
I
2
2
0
I 0 = √ 2I r.m.s
< I
2
>=
average value of I on an I
2
2
graph
− t
Time constant for circuits containing capacitance and resistance
τ = CR
CH13, Quantum Physics
h = 6.63×10
c = 3×10
8
−34
ms
−1
, Planck Constant
, Speed of Light in Free Space
Js
Einstein's Relation
E = hf
hc
E =
λ
Einstein's Photoelectric Equation
1
hf = ϕ +
2
hc
1
= ϕ +
λ
2
mv max
2
Momentum p of a Photon
E
2
mv max
E
p =
c
Energy of a photon, absorbed or emitted, as a result of an electron making a
transition between two energy levels E and E
1
2
hf = E 1 − E 2
hc
= E1 − E2
λ
De Brogile Wavelength
h
λ =
p
CH 14, Nuclear Physics
c = 3×10
8
ms
−1
, Speed of Light in Free Space
Einstein's Mass-Energy Equation
ΔE = Δmc
2
Atomic Mass Unit u to kilogram kg;
1 u = 1.660×10
−27
kg
Decay Constant
probability
λ =
time
Time can be measured in s , h , day
−1
−1
−1
Activity
A = −λN
N =
λ =
number of undecayed nuclei
the decay constant
and even year .
−1
ΔN
A =
Δt
ΔN =
the number of emissions (or decays)
Mathematical equation for Radioactive Decay
X = X 0 exp
−λt
X can be A (activity), N (number of undecayed nuclei) or R (count rate)
Decay Constant and Half-life relation
ln 2
λ =
0.693
=
t1
t1
2
2
CH 15, Medical Imaging
h = 6.63×10
−34
, Planck Constant
Js
Maximum Frequency of X-ray photons
eV
f max =
h
Intensity of X-ray
P
I =
A
P is power
A is cross-sectional area normal to radiation
Intensity at given Thickness of Material
I = I0 e
−μx
Acoustic Impedance of a Material
Z = ρc
ρ
is the density of material
Intensity Reflection fraction of the boundary between two materials.
Ir
=
I0
(Z 2 − Z 1 )
(Z 2 + Z 1 )
2
2
CH 16, Astronomy & Cosmology
H 0 = 2.4×10
−18
, Hubble's constant
Radiant Flux Density
L
F =
4πd
2
Wien's Displacement Law
λ max T = constant
Stefan-Boltzmann Law
2
L = 4πσr T
4
Hubble's Law
v = H0 d
v
is recession speed
Doppler Effect
Δf
Δλ
=
f
v
c
is Red Shift
v
=
λ
c