Physics data booklet
First assessment 2016
Diploma Programme
Physics data booklet
Published June 2014
Revised edition published November 2016
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4082
Contents
Mathematical equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Fundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Metric (SI) multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Equations—Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Equations—AHL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Equations—Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Physics data booklet
Physics data booklet
Mathematical equations
Area of a circle
A = πr 2 , where r is the radius
Circumference of a circle
C = 2πr , where r is the radius
Surface area of a sphere
A = 4πr 2 , where r is the radius
Volume of a sphere
4
V = πr 3 , where r is the radius
3
Physics data booklet
1
Fundamental constants
Quantity
2
Symbol
Approximate value
Acceleration of free fall
(Earth’s surface)
g
9.81m s−2
Gravitational constant
G
6.67 × 10−11 Nm2 kg−2
Avogadro’s constant
NA
6.02 × 1023 mol−1
Gas constant
R
8.31JK −1 mol−1
Boltzmann’s constant
kB
1.38 × 10−23 JK −1
Stefan–Boltzmann constant
σ
5.67 × 10−8 W m−2 K −4
Coulomb constant
k
8.99 × 109 Nm2 C−2
Permittivity of free space
ε0
8.85 × 10−12 C2 N−1 m−2
Permeability of free space
µ0
4π × 10−7 T m A −1
Speed of light in vacuum
c
3.00 × 108 m s−1
Planck’s constant
h
6.63 × 10−34 Js
Elementary charge
e
1.60 × 10−19 C
Electron rest mass
me
9.110 × 10−31 kg = 0.000549 u = 0.511MeV c −2
Proton rest mass
mp
1.673 × 10−27 kg = 1.007276 u = 938 MeV c −2
Neutron rest mass
mn
1.675 × 10−27 kg = 1.008665 u = 940 MeV c −2
Unified atomic mass unit
u
1.661× 10−27 kg = 931.5 MeV c −2
Solar constant
S
1.36 × 103 W m−2
Fermi radius
R0
1.20 × 10−15 m
Physics data booklet
Metric (SI) multipliers
Prefix
Abbreviation
Value
peta
P
1015
tera
T
1012
giga
G
109
mega
M
106
kilo
k
103
hecto
h
102
deca
da
101
deci
d
10 –1
centi
c
10 –2
milli
m
10 –3
micro
µ
10 –6
nano
n
10 –9
pico
p
10 –12
femto
f
10 –15
Unit conversions
1 radian (rad) ≡
180°
π
Temperature (K) = temperature (°C) + 273
1 light year (ly) = 9.46 × 1015 m
1 parsec (pc) = 3.26 ly
1 astronomical unit (AU) = 1.50 × 1011 m
1 kilowatt-hour (kWh) = 3.60 × 106 J
hc = 1.99 × 10−25 Jm = 1.24 × 10 −6 eV m
Physics data booklet
3
Electrical circuit symbols
cell
battery
ac supply
switch
voltmeter
4
V
ammeter
resistor
variable resistor
lamp
potentiometer
light-dependent
resistor (LDR)
thermistor
transformer
heating element
diode
capacitor
A
Physics data booklet
Equations—Core
Note: All equations relate to the magnitude of the quantities only. Vector notation has
not been used.
Sub-topic 1.2 – Uncertainties and errors
If: y = a ± b
then: ∆y = ∆a + ∆b
If: y =
then:
A
AV
ab
c
∆y
y
=
∆a ∆b ∆c
+
+
a
b
c
∆y
y
θ
= n
∆a
a
A V = A sin θ
Sub-topic 2.1 – Motion
1 2
at
2
v 2 = u 2 + 2as
s=
Sub-topic 2.2 – Forces
F = ma
v = u + at
s = ut +
AH
AH = A cos θ
If: y = a n
then:
Sub-topic 1.3 – Vectors and scalars
Ff ≤ µsR
Ff = µdR
(v + u ) t
2
Sub-topic 2.3 – Work, energy
and power
W = Fs cos θ
Sub-topic 2.4 – Momentum
and impulse
p = mv
EK =
1
mv 2
2
F=
Ep =
1
k ∆ x2
2
EK =
∆Ep = mg ∆h
power = Fv
efficiency =
=
∆p
∆t
p2
2m
impulse = F ∆t = ∆p
useful work out
total work in
useful power out
total power in
Physics data booklet
5
Sub-topic 3.1 – Thermal concepts
Q = mc ∆T
Sub-topic 3.2 – Modelling a gas
p=
F
A
n=
N
NA
Q = mL
pV = nRT
=
EK
Sub-topic 4.1 – Oscillations
T=
1
f
Sub-topic 4.2 – Travelling waves
c = fλ
Sub-topic 4.3 – Wave characteristics
I ∝ A2
I ∝ x −2
I = I 0 cos2 θ
6
3
3 R
=
kBT
T
2
2 NA
Sub-topic 4.4 – Wave behaviour
n1 sin θ 2 v 2
=
=
n2 sin θ1 v1
s=
λD
d
Constructive interference:
path difference = nλ
Destructive interference:


1
path difference =  n +  λ
2

Physics data booklet
Sub-topic 5.2 – Heating effect of
electric currents
Sub-topic 5.1 – Electric fields
I=
∆q
∆t
q1q2
r2
F =k
Kirchhoff’s circuit laws:
ΣV = 0 (loop)
ΣI = 0 (junction)
k=
1
4πε0
R=
V=
W
q
=
P V=
I I 2R =
E=
F
q
Rtotal = R1 + R2 + ...
I = nAvq
ε = I (R + r )
I
1
Rtotal
ρ=
Sub-topic 5.3 – Electric cells
V
=
V2
R
1
1
+
+ ...
R1 R2
RA
L
Sub-topic 5.4 – Magnetic effects of
electric currents
F = qvB sin θ
F = B IL sin θ
Sub-topic 6.2 – Newton’s law of
gravitation
Sub-topic 6.1 – Circular motion
v = ωr
F =G
a=
v 2 4 π2 r
= 2
r
T
g=
F=
mv 2
= mω 2 r
r
g =G
Physics data booklet
Mm
r2
F
m
M
r2
7
Sub-topic 7.1 – Discrete energy and
radioactivity
E =hf
λ=
Sub-topic 7.2 – Nuclear reactions
∆E = ∆mc 2
hc
E
Sub-topic 7.3 – The structure of matter
Charge
2
e
3
1
− e
3
Baryon
number
Quarks
u
d
c
s
t
1
3
b
1
3
Charge
Leptons
–1
e
µ
τ
0
νe
νµ
ντ
All leptons have a lepton number
of 1 and antileptons have a lepton
number of –1
All quarks have a strangeness number
of 0 except the strange quark that has
a strangeness number of –1
Particles
experiencing
Particles
mediating
Gravitational
Weak
Electromagnetic
Strong
All
Quarks,
leptons
Charged
Quarks,
gluons
Graviton
W + , W − , Z0
γ
Gluons
Sub-topic 8.2 – Thermal energy
transfer
Sub-topic 8.1 – Energy sources
power =
energy
time
P = eσ AT 4
power =
1
Aρv 3
2
λmax (metres) =
I=
power
A
albedo =
8
2.90 × 10−3
T (kelvin)
total scattered power
total incident power
Physics data booklet
Equations—AHL
Sub-topic 9.1 – Simple harmonic
motion
ω=
2π
T
Sub-topic 9.2 – Single-slit diffraction
θ=
λ
b
a = −ω 2 x
Sub-topic 9.3 – Interference
x = x0 sin ω t ; x = x0 cos ω t
nλ = d sin θ
v = ω x0 cos ω t ; v = −ω x0 sin ω t
1

Constructive interference: 2dn =  m +  λ
2

v = ±ω ( x0 2 − x 2 )
Destructive interference: 2dn = mλ
EK =
1
mω 2 ( x0 2 − x 2 )
2
ET =
1
mω 2 x0 2
2
pendulum: T = 2π
l
g
mass-spring:T = 2π
m
k
Sub-topic 9.4 – Resolution
θ = 1.22
R=
λ
b
λ
= mN
∆λ
Sub-topic 9.5 – Doppler effect
 v 
Moving source: f ′ = f 

 v ± us 
 v ± uo 
Moving observer: f ′ = f 

 v 
∆f
f
Physics data booklet
=
∆λ
λ
≈
v
c
9
Sub-topic 10.1 – Describing fields
W = q ∆Ve
W = m∆Vg
Sub-topic 10.2 – Fields at work
GM
r
Ve =
∆Vg
∆r
E=−
Vg = −
g=−
Ep = mVg = −
Fg =
10
GMm
r2
v esc =
2GM
r
v orbit =
GM
r
kQ
r
∆Ve
∆r
GMm
kQq
=
Ep qV
=
e
r
r
Fe =
kQq
r2
Physics data booklet
Sub-topic 11.1 – Electromagnetic
induction
Φ = BA cos θ
∆Φ
∆t
ε = −N
ε = Bv l
Sub-topic 11.3 – Capacitance
C=
q
V
Cparallel = C1 + C2 + ...
1
Cseries
ε = Bv l N
1
1
+
+ ...
C1 C2
=
A
Sub-topic 11.2 – Power generation and
C =ε
transmission
d
I0
Irms =
E=
2
V0
Vrms =
1
CV 2
2
τ = RC
2
V0
V
R = = rms
I 0 Irms
q = q0 e
Pmax = I 0V0
I = I0e
1
I 0V0
2
V = V0 e
P=
−
−
t
τ
t
τ
−
t
τ
ε p Np I s
=
=
ε s Ns I p
Sub-topic 12.1 – The interaction of
matter with radiation
Sub-topic 12.2 – Nuclear physics
1
E =hf
R = R0 A 3
Emax = h f − Φ
N = N0 e − λ t
E=−
13.6
eV
n2
mvr =
nh
2π
A = λ N0 e − λ t
sin θ ≈
λ
D
2
P (r ) = ψ ∆V
∆ x∆p ≥
h
4π
∆E ∆t ≥
h
4π
Physics data booklet
11
Equations—Options
Sub-topic A.1 – The beginnings of
relativity
x′ = x − v t
Sub-topic A.2 – Lorentz
transformations
1
γ=
1−
u′ = u − v
Sub-topic A.3 – Spacetime diagrams
v 
θ = tan−1  
c
v2
c2
x′ = γ ( x − vt ); ∆ x′ = γ ( ∆ x − v ∆t )
vx 
; ∆t ′ = γ
c 2 


t′ = γ t −
v∆x 

 ∆t − c 2 


u −v
uv
1− 2
c
u′ =
∆t = γ ∆t0
L=
L0
γ
(ct ′)2 − ( x′)2 = (ct )2 − ( x )2
Sub-topic A.4 – Relativistic mechanics
(HL only)
E = γ m0 c 2
E0 = m0 c 2
EK = (γ − 1) m0 c 2
p = γ m0v
E 2 = p 2c 2 + m0 2c 4
Sub-topic A.5 – General relativity
(HL only)
∆f
=
g ∆h
c2
Rs =
2GM
c2
f
∆t =
∆t0
1−
Rs
r
qV = ∆EK
12
Physics data booklet
Sub-topic B.1 – Rigid bodies
and rotational dynamics
Γ = Fr sin θ
I = ∑ mr 2
Γ = Iα
ω = 2πf
ωf = ωi + α t
ω f2 = ω 2i + 2αθ
1
θ = ωi t + α t 2
2
L = Iω
EKrot =
1 2
Iω
2
Sub-topic B.3 – Fluids and fluid
dynamics (HL only)
Sub-topic B.2 – Thermodynamics
Q = ∆U + W
3
nRT
2
U=
∆S =
∆Q
T
5
pV 3 = constant (for monatomic gases)
W = p∆V
η=
useful work done
energy input
ηCarnot = 1 −
Tcold
Thot
Sub-topic B.4 – Forced vibrations and
resonance (HL only)
energy stored
energy dissipated per cycle
B = ρ fVf g
Q = 2π
P = P0 + ρ f gd
Q = 2π × resonant frequency ×
energy stored
power loss
Av = constant
1 2
ρv + ρ gz + p = constant
2
FD = 6πη rv
R=
vr ρ
η
Physics data booklet
13
Sub-topic C.1 – Introduction to
imaging
1
f
=
1 1
+
v u
Sub-topic C.2 – Imaging
instrumentation
fo
fe
M=
1
P=
Sub-topic C.3 – Fibre optics
f
n=
h
v
m= i =−
ho
u
M=
attenuation = 10 log
θi
θo
Mnear point =
1
sin c
D
f
+ 1; Minfinity =
Sub-topic C.4 – Medical imaging
(HL only)
D
f
I
I0
LI = 10 log
I1
I0
I = I0e − µ x
µ x 1 = In2
2
Z = ρc
Sub-topic D.1 – Stellar quantities
d (parsec) =
1
p (arc-second)
L = σ AT 4
b=
Sub-topic D.2 – Stellar characteristics
and stellar evolution
λmaxT = 2.9 × 10−3 mK
L ∝ M 3 .5
L
4πd 2
Sub-topic D.3 – Cosmology
Sub-topic D.5 – Further cosmology
(HL only)
z=
∆λ v
≈
λ0 c
v=
4πG ρ
r
3
z=
R
−1
R0
ρc =
3H 2
8πG
v = H0 d
T ≈
14
1
H0
Physics data booklet