Download Data and Formulae Booklet The following equations and formulae

AM Syllabus: (2013): Physics
Data and Formulae Booklet
The following equations and formulae may be useful in answering some of the questions in the
examination.
Uniformly accelerated motion:
Ray optics:
Refractive index: n1 sin θ1 = n 2 sin θ 2
v = u + at
1
s = ut + at 2
2
v 2 = u 2 + 2as
⎛u+v⎞
s=⎜
⎟t
⎝ 2 ⎠
Useful formulae:
1
1 n3
d (mv)
dt
F=
Power:
P = Fv
Momentum:
p = mv
Magnification:
sin θ 1 v1
=
sin θ 2 v 2
= 1 n2 . 2 n3
1 1 1
= + (real is positive)
f
u v
1 1 1
= − (Cartesian)
f
v u
Thin lenses:
Mechanics:
Newton’s second law:
n2 =
m=
v hi
=
(real is positive)
u ho
m=−
h
v
= − i (Cartesian)
u
ho
Current electricity:
Circular motion and rotational dynamics:
Torque:
dθ
=
dt
dω
α=
=
dt
mv 2
F=
r
τ = Iα
Work done in rotation:
τθ = Δ
ω=
Angular speed:
Angular acceleration:
Centripetal force:
(
1
2
v
r
a
r
Iω2
)
x = xo sin(ωt + φ)
Velocity:
v = ω xo cos(ωt + φ)
v = ± ω xo 2 − x 2
a = –ω2 x
1 2π
T = =
f
ω
Mass on a light spring: T = 2π
Resistors in series:
RTOTAL = R1 + R2 + …
1
RTOTAL
Power:
P = IV
Resistivity:
ρ=
Temperature coefficient: α =
=
1
1
+
+ ...
R1 R 2
RA
l
Rθ − R 0
R 0θ
Alternating current:
Displacement:
Period:
I = nAve
Resistors in parallel:
Simple harmonic motion:
Acceleration:
Current:
For sinusoidal alternating current:
I = Io sin2πft
Root mean square for sinusoidal alternating
I
V
I rms = 0 ; V rms = 0
current and voltage:
2
2
Reactance: X L = 2πfL ; X C = 1 (2πfC )
m
k
1
AM Syllabus: (2013): Physics
Capacitance:
Stationary waves:
v= T
Speed of waves on strings:
Capacitance of parallel plates: C =
μ
Capacitors in parallel:
Wave motion:
s=
Two slit interference:
Capacitors in series:
λD
Diffraction grating:
d
d sinθ = nλ
Single slit diffraction:
θ=
λ
a
Charging:
Diffraction of circular aperture:
sin θ ≈ θ = 1.22
λ
a
Uniform field:
Force between point charges:
F
dV
=−
dr
+q
F
V
E=
=
+q d
E=
F=
Q1Q 2
4πε 0 r 2
Electric field strength of a point charge:
Q
E=
4πε 0 r 2
Force between point masses:
Electric potential:
Gravitational potential:
Work:
Discharging:
d
C = C1 + C2 +…
1
1
1
=
+
+ ...
C C1 C 2
1
W = CV 2
2
−t
⎛
⎞
Q = Q0 ⎜ 1 − e RC ⎟
⎝
⎠
Q = Q0 e
−t
RC
Inductance:
Fields:
Electric field strength:
Energy stored:
ε 0ε r A
M 1M 2
r2
Q
V=
4πε 0 r
GM
VG = −
r
F =G
W = QV
Mutual inductance:
Self inductance:
Energy stored:
E
dI
dt
E
L=−
dI
dt
1 2
W = LI
2
M =−
Electromagnetism:
Force on wire:
F = BIl
Torque on a rectangular coil: τ = BANI
Force on moving charge:
F = BQv
Magnetic flux:
Φ = BA
Field inside a solenoid:
B = μ0 μr nI
Field near a long straight wire: B = μ0
Induced emf:
I
2π r
E = −N
dΦ
dt
Emf induced in a moving conductor:
E = Blv
Simple alternator emf:
V = V0 sin( ωt + φ )
Hall voltage:
VH =
BI
nQt
2
AM Syllabus: (2013): Physics
Temperature:
Materials:
Temperature (K): T = 273.16
Celsius scale:
P
K
Ptr
F = kΔx
F
σ =
A
Δl
ε=
l
σ
Y=
ε
Hooke's law:
θ (°C) = T (K) – 273.15 K
Stress:
Strain:
Young's modulus:
E = 12 k ( Δl )
Energy stored in a stretched wire:
First and second laws of thermodynamics:
First law of thermodynamics:
ΔU = ΔQ + ΔW
Ideal heat engine:
η = 1−
Gases:
Ideal gas equation:
Kinetic theory of an ideal gas:
PV =
Boltzmann's constant: k =
1
Nm < c 2 >
3
R
NA
Principal molar heat capacities of an ideal gas:
γ =
Adiabatic process:
Heat transfer:
Thermal conduction:
Tc
Th
PV = nRT
CP
; CP – CV = R
CV
2
dQ
dθ
= −kA
dt
dx
Quantum phenomena:
Quantum energy:
E = hf
Mass-energy
E = mc2
Energy levels:
⎛1
⎞
hf = Φ + ⎜ mv2 ⎟
⎝2
⎠ max
hf = E2− E1
De Broglie wavelength:
λ=
Photoelectric effect:
h
mv
Radioactivity:
Decay rate:
PVγ = Constant
dN
= − λN ; A = λ N
dt
N = No e−λt
Half-life:
T1 =
2
ln 2
λ
Absorption law for gamma radiation:
I = Io e−μd
3
AM Syllabus: (2013): Physics
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
Logarithms:
ln x n = n ln x
4 3
πr
3
( )
( )
ln e kx = kx
Equation of a straight line:
y = mx + c
Relationship between cosine and sine:
sin ( 90° − θ ) = cos θ
Small angles:
sin θ ≈ tan θ ≈ θ (in radians)
cos θ ≈ 1
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
Boltzmann constant k = 1.38 × 10−23 J K−1
Molar gas constant R = 8.31 J K−1 mol−1
Avogadro’s constant NA = 6.02 × 1023 mol−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
Permeability of free space μo = 4π × 10−7 H 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
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