Physics data booklet
For use during the course and in the examinations
First assessment 2025
Version 1.0
Annotated by Jaya Ramchandani https://www.teacherspayteachers.com/Store/Ibdp-Physics
Diploma Programme
Physics data booklet
Published February 2023
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4082
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Mathematical equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Fundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Metric (SI) multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Electromagnetic spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
A. Space, time and motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
B. The particulate nature of matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
C. Wave behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
D. Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
E. Nuclear and quantum physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Physics data booklet
This page is intentionally blank.
Physics data booklet
Introduction
This Diploma Programme (DP) Physics data booklet accompanies the DP Physics guide and DP
Physics teacher support material. It contains electrical symbols, mathematics equations, constants,
and physics equations relevant to the course.
Students must have access to a copy of this booklet for the duration of the course so that they
can become familiar with its contents. Direct reference is made to relevant equations in the
“Understandings” sections of the guide. This helps to maintain the emphasis on interpretation and
application rather than memorization of symbols, constants and equations.
The Physics data booklet is split into two sections. The first includes information which is used
throughout the teaching of DP physics and the second contains equations relevant to specific themes
and topics. Note that all equations relate to the magnitude of the quantities only. Vector notation has
not been used.
Each student must have access to a clean copy of the Physics data booklet during examinations.
It is the responsibility of the school to download a copy of this booklet from IBIS or the Programme
Resource Centre and to ensure that there are sufficient copies available for all students.
Physics data booklet
1
Mathematical equations
1
(bh ) where b is the base, h is the height
2
Area of a triangle
A=
Area of a circle
A = πr 2 where r is the radius
Circumference of a circle
C = 2πr
Volume of a cuboid
V = lwh where l is the length, w is the width, h is the
height
Volume of a cylinder
V
Volume of a prism
V = Ah where A is the area of cross-section
Volume of a sphere
V=
4 3
πr
3
Area of the curved surface
of a cylinder
A
2 rh
Vectors
r 2h
A
AV
θ
Trigonometric relationships
AH
A cos
AV
A sin
tan θ =
AH
sin θ
cos θ
sin2 θ + cos2 θ = 1
2
Physics data booklet
Uncertainties
If: y = a ± b
then: ∆y = ∆a + ∆b
ab
c
then:
∆y ∆a ∆b ∆c
=
+
+
y
a
b
c
If: y = a n
then:
∆y
∆a
= n
y
a
If: y =
Fundamental constants
Quantity
Symbol
Approximate value
Acceleration of free fall
g
9.8 m s−2 (Earth’s surface)
Gravitational constant
G
6.67 × 10−11 Nm2 kg−2
Avogadro constant
NA
6.02 × 1023 mol−1
Gas constant
R
8.31JK −1 mol−1
Boltzmann 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
4π × 10−7 T mA −1
Speed of light in vacuum
c
3.00 × 108 m s−1
Planck 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
3
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
h c = 1.99 × 10−25 Jm = 1.24 × 10 −6 eV m
4
Physics data booklet
Electrical circuit symbols
Cell
Battery
Switch
Voltmeter
Ammeter
Resistor
Variable resistor
Light-dependent resistor
(LDR)
Thermistor
Potentiometer
Lamp
Light emitting diode (LED)
Heating element
Motor
Earth (ground)
Electromagnetic spectrum
energy
10 −16
10 −14
 rays
10 −12
10 −10
X-rays
10 −8
UV
10 −6
IR
10 −4
10 −2
microwaves
100
102
10 4
106
108 wavelength / m
radio waves
V I B G Y O R
400
700
wavelength / nm
Physics data booklet
5
A. Space, time and motion
Standard level and higher level
A.1 Kinematics
s
u
v
a
=
=
=
=
displacement
initial velocity
final velocity
acceleration
s=
u +v
t
2
v = u + at
s = ut +
1 2
at
2
v 2 = u 2 + 2as
A.2 Forces and momentum
Ff
µs
µd
FN
FH
k
x
Fd
η
r
v
Fb
ρ
V
g
Fg
p
J
F
m
a
ω
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
T =
force of friction
static friction coeff.
dynamic friction coeff.
normal force
spring force
spring constant
change in position
drag
drag coeff.
radius
linear velocity
buoyant force
fluid density
fluid volume
acc. due to grav.
weight (grav. force)
momentum
impulse
force
mass
acceleration
angular velocity
angular frequency
period
A.3 Work, energy and power
W
F
s
θ
Ek
m
v
p
Ep
g
h
EH
k
x
P
η
6
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
work done / energy transferred
force
displacement
angle between F-vector & s-vector
kinetic energy
mass
velocity
momentum
gravitational potential energy
acceleration due to grav.
height
elastic potential energy
spring constant
change in position
power
Efficiency
Ff ≤ µsFN
Ff = µdFN
FH = −k x
Fd = 6πη rv
Fb = ρVg
Fg = mg
p = mv
J = F ∆t
F = ma =
∆p
∆t
a=
v2
4π 2 r
= ω 2r = 2
r
T
v=
2π r
= ωr
T
W = Fs cos θ
1
p2
mv 2 2
2m
Ek ∆Ep = mg ∆h
EH =
P=
η=
1
k ∆x 2
2
∆W
= Fv
∆t
Eoutput
Einput
=
Poutput
Pinput
Physics data booklet
Additional higher level
A.4 Rigid body mechanics
τ
F
r
θ
Δθ
ωf
ωi
t
α
I
L
ω
Ek
=
=
=
=
=
=
=
=
=
=
=
=
=
torque
force
radius
angle between F-vector & lever
angular displacement
final angular velocity
initial angular velocity
time
angular acc.
moment of inertia
angular momentum
angular velocity
kinetic energy
τ = Fr sin θ
∆θ =
ωf + ωi
t
2
ωf = ωi + α t
1
∆θ = ωit + α t 2
2
ωf2 = ωi2 + 2α∆θ
I = Σmr 2
τ = Iα
L = Iω
∆L = τ∆t
∆L = ∆( I ω )
Ek =
1 2 L2
Iω =
2
2I
A.5 Galilean and special relativity
x ' = x − vt
x’
x
t’
t
v
=
=
=
=
=
t'=t
u’
u
γ
c
Δs
Δt
Δx
t0
L
L0
θ
=
=
=
=
=
=
=
=
=
=
=
v =
position in 2nd ref. frame
position in 1st ref. Frame
time in 2nd ref. frame
time in 1st ref. frame
relative vel. of 2nd ref. frame
to 1st ref. frame
velocity in 2nd ref. frame
velocity in 1st ref. frame
gamma factor
speed of light
space-time interval
time interval (dilation)
change in position
proper time interval
length (contraction)
proper length
angle between world line & time
axis
speed of object
u' = u −v
x ' = γ ( x − vt ) where γ =
1
1−
v2
c2
 vx 
t ' = γ t − 2 
c 

u' =
u −v
uv
1− 2
c
( ∆s )2 = (c ∆t )2 − ∆x 2
∆t = γ∆t0
L=
L0
γ
tan θ =
Physics data booklet
v
c
7
B. The particulate nature of matter
Standard level and higher level
B.1 Thermal energy transfers
ρ
m
V
Ek
kB
T
Q
c
ΔT
L
Δt
k
A
Δx
L
σ
A
b
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
density
mass
volume
average kinetic energy
Boltzmann constant
absolute temperature
thermal energy
specific heat capacity
change in temperature
specific latent heat
change in time
thermal conductivity
cross-sectional area (wire)
conducting distance
luminosity (power)
Stefan-Boltzmann constant
surface area of sphere
brightness (intensity)
λmax = max intensity at this
ρ=
m
V
Ek =
3
kBT
2
Q = mc ∆T
Q = mL
∆Q
∆T
= kA
∆t
∆x
L = σ AT 4
b=
L
4π d 2
λmaxT = 2.9 × 10−3 mK
B.2 Greenhouse effect
emissivity =
σ = Stefan-Boltzmann constant
T = absolute temperature
albedo =
B.3 Gas laws
P
F
A
n
N
NA
V
T
V
kB
R
ρ
v
U
=
=
=
=
=
=
=
=
=
=
=
=
=
=
pressure
force perpendicular to surf.
surface area
number of moles
number of particles
Avogadro constant
volume
absolute temperature
volume
Boltzmann constant
gas constant
density
average velocity
internal energy
P=
F
A
n=
N
NA
total scattered power
total incident power
PV
= constant
T
=
PV nRT
= NkBT
P=
=
U
8
power radiated per unit area
σT 4
1 2
ρv
3
3
3
=
nRT
NkBT
2
2
Physics data booklet
B.5 Current and circuits
I
q
t
V
=
=
=
=
R
ρ
A
L
P
ε
=
=
=
=
=
=
current
charge
time
potential difference
(voltage)
resistance
resistivity
cross-sectional area
length
power
emf of cell
I=
∆q
∆t
V=
W
q
R=
V
I
ρ=
RA
L
V2
=
P I=
V I R=
R
2
Series circuits
Parallel circuits
I= I=
I 2 = ...
1
I = I1 + I 2 + ...
V = V1 + V2 + ...
V= V=
V2 = ...
1
Rs = R1 + R2 + ...
1
1
1
=
+
+ ...
Rp R1 R2
ε = I(R + r )
Additional higher level
B.4 Thermodynamics
Q = ∆U + W
Q
ΔU
W
P
ΔV
n
R
ΔT
N
kB
ΔS
Ω
η
Tc
Th
W = P ∆V
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
thermal energy
change in internal energy
work done
pressure
change in volume
number of moles
gas constant
change in temperature
number of particles
Boltzmann constant
change in entropy
number of microstates
efficiency
temp. of cold reservoir
temp. of hot reservoir
∆U =
∆S =
3
3
nR ∆T = NkB ∆T
2
2
∆Q
T
S = kB ln Ω
5
3
PV = constant
η=
useful work
input energy
ηCarnot = 1 −
Physics data booklet
Tc
Th
9
C. Wave behaviour
Standard level and higher level
C.1 Simple harmonic motion
a
T
f
ω
m
k
l
g
=
=
=
=
=
=
=
=
acceleration
period
frequency
angular frequency
mass
spring constant
length
acceleration due to gravity
C.2 Wave model
v = wave speed
f = frequency
λ = wavelength
C.3 Wave phenomena
n1
n2
θ1
θ2
v1
v2
n
λ
s
d
=
=
=
=
=
=
=
=
=
=
refractive index of medium 1
refractive index of medium 2
angle of incidence
angle of refraction
wave speed in medium 1
wave speed in medium 2
integer (1, 2, 3…)
wavelength
fringe width
slit width
a = −ω 2 x
T=
1 2π
=
f
ω
T = 2π
m
k
T = 2π
l
g
v= fλ =
λ
T
n1 sin θ 2 v 2
=
=
n2 sin θ1 v1
Constructive interference:
path difference = nλ
Destructive interference:
1
path difference = (n + )λ
2
λD
d
∆f ∆λ v
=
≈
f
λ
c
s=
C.5 Doppler effect
f = frequency
λ = wavelength
v = wave speed
Additional higher level
C.1 Simple harmonic motion
x
x0
ω
t
φ
v
ET
m
10
=
=
=
=
=
=
=
=
displacement
max. displacement
angular frequency
time
phase angle
velocity at time t
total energy
mass
x = x0 sin(ωt + φ )
v = ω x0 cos(ωt + φ )
v = ±ω x0 2 − x 2
ET =
1
mω 2 x02
2
Ep =
1
mω 2 x 2
2
Physics data booklet
C.3 Wave phenomena
n = order of maxima (1, 2, 3…)
θ = angle between maxima and normal
d = distance between slits
→
C.5 Doppler effect
f’
f
v
us
uo
=
=
=
=
=
observed frequency
emitted frequency
velocity of the wave
velocity of the source
velocity of the observer
Physics data booklet
θ=
λ
b
←
nλ = d sin θ
θ = angle between central
max and 1st dark fringe
λ = wavelength
b = slit width

v 

 v ± us 
Moving source: f ′ = f 
 v ± uo 
Moving observer: f ′ = f 

 v 
11
D. Fields
Standard level and higher level
D.1 Gravitational fields
F
G
m
r
=
=
=
=
gravitational force
universal gravitational constant
mass
distance between point masses
D.2 Electric and magnetic fields
F
K
q
r
E
V
=
=
=
=
=
=
electric force
Coulomb constant
charge
distance between point charges
Electric field strength
potential difference (|| plates)
D.3 Motion in electromagnetic fields
F
q
v
B
I
L
=
=
=
=
=
=
magnetic force
charge
velocity
magnetic field strength
current
length of conductor
m1m2
r2
F =G
=
g
F
M
= G 2
m
r
F =k
E=
F
q
E=
V
d
q1q2
1
where k =
2
4πε 0
r
F = qvB sin θ
←
F = B I L sin θ ←
II
F
= µ0 1 2
2π r
L
←
θ
= angle between
velocity and field
θ = angle between
current and field
µ0 = permeability of
free space
Additional higher level
D.1 Gravitational fields
Ep
G
m
r
Vg
M
g
W
v
=
=
=
=
=
=
=
=
=
gravitational potential energy
universal gravitational constant
mass
distance between point masses
gravitational potential
mass of source of field
acceleration due to gravity
work done
velocity
Ep = −G
m1m2
r
Vg = −G
M
r
g=−
∆Vg
∆r
W = m∆Vg
2GM
r
v esc =
v orbital =
D.2 Electric and magnetic fields
Ep
k
q
r
Ve
Q
E
W
=
=
=
=
=
=
=
=
electric potential energy
Coloumb constant
charge
distance between point charges
electric potential
charge of source of field
electric field strength
work done
Ep = k
Ve =
GM
r
q1q2
r
kQ
r
E=−
∆Ve
∆r
W = q ∆Ve
12
Physics data booklet
D.4 Induction
φ
B
A
θ
=
=
=
=
magnetic flux
magnetic field strength
area
angle between flux lines and
the normal to the area, A
Φ = BA cos θ
ε = −N
∆Φ
∆t
ε = BvL
ε
N
t
v
=
=
=
=
induced emf
number of turns
time
velocity of moving
conductor
L = length of moving
conductor
E. Nuclear and quantum physics
Standard level and higher level
E.1 Structure of the atom
E =hf
E = photon energy f = frequency
E.3 Radioactive decay
E = mc 2
E = energy m = mass
E.5 Fusion and stars
d(parsec) =
1
d = distance
p(arc-second)
Additional higher level
E.1 Structure of the atom
R
R0
A
E
n
=
=
=
=
=
radius of nucleus
Fermi radius
nucleon number
energy (in eV)
energy level
E.2 Quantum physics
h
f
ϕ
λ
=
=
=
=
Planck constant
frequency
work function of the metal
wavelength (scattered, f;
incident, i)
p = momentum
me = electron rest mass
E.3 Radioactive decay
N =
N0 =
λ =
t =
A =
T1/2
remaining undecayed nuclei
initial undecayed nuclei
decay constant
time
activity
= half life
Physics data booklet
1
R = R0 A 3
13.6
eV
n2
m
v
nh
← r
mvr =
2π
h
E=−
Emax = h f − Φ
λ=
=
=
=
=
mass of e
linear speed of e
distance from nucleus
Planck constant
←
Emax = maximum KE of
photoelectron
h
p
λf − λi = ∆λ =
c = speed of light
θ = photon scattering
angle
←
h
(1 − cos θ )
me c
N = N0 e − λ t
A = λ N = λ N0 e − λ t
T1 =
2
ln 2
λ
13