IB Physics Formula booklet equations

SUVAT

(A.1 Kinematics)

S= displacement (m)

u= initial velocity (m/s)

v= final velocity (m/s)

a= acceleration (m/s²)

t= time (s)

Ff≤μsFN

(A.2 Forces and Momentum)

Body is stationary

Ff: Frictional force (N)

μs: Coefficient of static friction

FN= Normal reaction force (N)

Ff​=μd​FN​

(A.2 Forces and Momentum)

Body is in motion

Ff​: Kinetic friction force (N)

μd​: Coefficient of dynamic (kinetic) friction

FN​: Normal force (N)

F=−kx

(A.2 Forces and Momentum)

Spring

F: Restoring force (N)

k: Spring constant (N/m)

x: Displacement from equilibrium (m)

Fd=6πηrv

(A.2 Forces and Momentum)

F: Drag force (N)

η: Viscosity of the fluid (Pa·s)

r: Radius of the object (m)

v: Velocity of the object (m/s)

Fb=ρVg

(A.2 Forces and Momentum)

F: Buoyant force (N)

ρ: Density of the fluid (kg/m³)

V: Volume of the object submerged (m³)

g: Gravitational field strength (9.8 m/s²)

F = ma= Δp​/Δt

(A.2 Forces and Momentum)

F: Resultant force (N)

m: mass (kg)

a: acceleration (m/s²)

Δp: Change in momentum (kg·m/s)

Δt: Time interval (s)

J = F∆t = ∆p

(A.2 Forces and Momentum)

J: Impulse (N·s)

F: Force (N)

Δt: Time duration (s)

p = mv

(A.2 Forces and Momentum)

p: Momentum (kg·m/s)

m: Mass (kg)

v: Velocity (m/s)

a= v²/r

a=ω²r

a=4πr²/T²

(A.2 Forces and Momentum)

a: Centripetal acceleration (m/s²)

v: Velocity (m/s)

r: Radius of circular path (m)

ω: Angular velocity (rad/s)

T: Period (s)

v=2πr/T

v=ωr

(A.2 Forces and Momentum)

Velocity of a body traveling in a circle

v: Linear velocity (m/s)

ω: Angular velocity (rad/s)

r: Radius of circular motion (m)

T: Period (s)

W = Fscosθ

(A.3 Work, Energy, and Power)

Work done (Nm) = Force (N) x displacement (m) x cos (angle to the force (°))

- When θ=90° No work is done

Ek​=½​mv²

Ek= p²/2m

(A.3 Work, Energy, and Power)

Body in motion

Ek​: Kinetic energy (J)

m: Mass (kg)

v: Velocity (m/s)

p= momentum

ΔEp​=mgh

(A.3 Work, Energy, and Power)

Gravitational potential energy changes when an object's height changes in a gravitational field.

ΔEp​: Change in gravitational potential energy (J)

m: Mass (kg)

g: Gravitational field strength (9.8 m/s²)

Δh: Change in height (m)

EH=½​k(Δx)²

(A.3 Work, Energy, and Power)

Elastic potential energy is stored in a stretched or compressed spring.

E: Elastic potential energy (J)

k: Spring constant (N/m)

Δx: Displacement from equilibrium (m)

P=W​/Δt=Fv

(A.3 Work, Energy, and Power)

Power: rate of energy transfer

P: Power (W)

W: Work done (J)

Δt: Time interval (s)

F: Force (N)

v: Velocity (m/s)

η

(A.3 Work, Energy, and Power)

η: Efficiency

ρ=m/V

(B.1 Thermal Energy Transfers)

ρ: Density (kg/m³)

m: Mass (kg)

V: Volume (m³)

Ek​=3/2× ​kB​×T

(B.1 Thermal Energy Transfers)

Ek​: Average kinetic energy of a particle (J)

kB: Boltzmann constant

T: Absolute temperature (K)

Q=mcΔT

(B.1 Thermal Energy Transfers)

Material changing temperature

Q: Heat transferred (J)

m: Mass (kg)

c: Specific heat capacity (J/kg°C)

ΔT: Change in temperature (K or °C)

Q=mL

(B.1 Thermal Energy Transfers)

Material changing phase

Q: Heat transferred (J)

m: Mass (kg)

L: Specific latent heat (J/kg)

ΔQ​/Δt=(kA) ΔT​/Δx

(B.1 Thermal Energy Transfers)

Heat conduction through a material

ΔQ/Δt: Rate of heat transfer (W)

k: Thermal conductivity (W/mK)

A: Cross-sectional area (m²)

ΔT: Temperature difference (K)

Δx: Thickness of the material (m)
ΔT/Δx: Temperature gradient (K/m)

L=σT⁴A

(B.1 Thermal Energy Transfers)

L: Total power radiated/Luminosity (W)

σ: Stefan-Boltzmann constant

T: Absolute temperature (K)

A: Surface area (m²)

b=L/4πd²

(B.1 Thermal Energy Transfers)

b: Intensity/apparent brightness (W/m²)

L: Luminosity (W)

d: Distance from the source (m)

λmax​T=2.9×10−3mK

(B.1 Thermal Energy Transfers)

Wein's Law

λmax​: Wavelength of maximum intensity (m)

T: Absolute temperature (K)

P=F​/A

(B.3 Gas Laws)

P: Pressure (Pa)

F: Force (N)

A: Area (m²)

n=N​/NΑ

(B.3 Gas Laws)

n: Amount of substance (mol)

N: Number of particles

NA​: Avogadro's constant

PV/T​=constant

(B.3 Gas Laws)

P: Pressure (Pa)

V: Volume (m³)

T: Absolute temperature (K)

PV=nRT

PV=NkB​T

(B.3 Gas Laws)

IDEAL GAS LAW

P: Pressure (Pa)

V: Volume (m³)

n: Number of moles (mol)

R: Gas constant

T: Absolute temperature (K)

N: Number of particles

kB​: Boltzmann constant

P=1/3×ρv²

(B.3 Gas Laws)

P: Pressure (Pa)

ρ: Density of the gas (kg/m³)

v: Velocity of gas particles (m/s)

U=3/2×nRT

U= 3/2×​NkB​T

(B.3 Gas Laws)

U: Internal energy (J)

n: Number of moles (mol)

R: Gas constant

T: Absolute temperature (K)

N: Number of particles

kB: Boltzmann constant

Q=ΔU+W

(B.4 Thermodynamics)

Q: Heat added to the system (J)

ΔU Change in internal energy (J)

W: Work done by the system (J)

W=PΔV

(B.4 Thermodynamics)

W: Work done (J)

P: Pressure (Pa)

ΔV: Change in volume (m³)

ΔU=(3/2)×​nRΔT

ΔU=(3/2)×​NkB​ΔT

(B.4 Thermodynamics)

ΔU: Change in internal energy (J)

n: Number of moles (mol)

R: Gas constant

ΔT: Change in temperature (K)

N: Number of particles

kB​: Boltzmann constant

ΔS=ΔQ/T

(B.4 Thermodynamics)

ΔS: Change in entropy (J/K)

ΔQ: Heat transfer (J)

T: Absolute temperature (K)

S=kB​lnΩ

(B.4 Thermodynamics)

S: Entropy (J/K)

kB​: Boltzmann constant

Ω: Number of microstates

PV⁵/₃​=constant

(B.4 Thermodynamics)

For adiabatic processes in a monatomic ideal gas

P: Pressure (Pa)

V: Volume (m³)

ηCarnot​=1−Th​/Tc​​

(B.4 Thermodynamics)

Carnot efficiency is the maximum efficiency of a heat engine.

ηCarnot​: Carnot efficiency

Tc​: Temperature of the cold reservoir (K)

Th​: Temperature of the hot reservoir (K)

I=Δq​/Δt

(B.5 Current and Circuits)

I: Electric current (A)

Δq: Electric charge (C)

Δt: Time interval (s)

V=W/q

(B.5 Current and Circuits)

V: Electric potential difference (V)

W: Work done or energy transferred (J)

q: Charge (C)

R=V/I​

(B.5 Current and Circuits)

R: Resistance (Ω)

V: Voltage (V)

I: Current (A)

ρ=RA/L

(B.5 Current and Circuits)

resistivity of a material

ρ: Resistivity (Ωm)

R: Resistance (Ω)

A: Cross-sectional area (m²)

L: Length of the conductor (m)

P=VI=I²R=V²/R

(B.5 Current and Circuits)

Electrical power

P: Power (W)

V: Voltage (V)

I: Current (A)

R: Resistance (Ω)

ε=I(R+r)

(B.5 Current and Circuits)

ε: Electromotive force (e.m.f) (V)

I: Current (A)

R: External resistance (Ω)

r: Internal resistance of the source (Ω)

a=−ω²/x

(C.1 Simple Harmonic Motion)

a: Acceleration (m/s²)

ω: Angular frequency (rad/s)

x: Displacement from equilibrium (m)

T=1​/f

T=2π​/ω

(C.1 Simple Harmonic Motion)

The period of oscillation

T: Period (s)

f: Frequency (Hz)

ω: Angular frequency (rad/s)

T=2π√m​​/k

(C.1 Simple Harmonic Motion)

The period of a mass-spring system

T: Period (s)

m: Mass (kg)

k: Spring constant (N/m)

T=2π√l​​/g

(C.1 Simple Harmonic Motion)

The period of a simple pendulum

T: Period (s)

l: Length of the pendulum (m)

g: Gravitational field strengt (m/s²)

x=x₀​sin(ωt+ϕ)

(C.1 Simple Harmonic Motion)

The displacement in SHM

x: Displacement (m)

x₀: Amplitude (m)

ω: Angular frequency (rad/s)

t: Time (s)

ϕ: Phase constant (rad)

v=ωx₀​cos(ωt+ϕ)

(C.1 Simple Harmonic Motion)

v: Velocity (m/s)

x₀​: Amplitude (m)

ω: Angular frequency (rad/s)

t: Time (s)

ϕ: Phase constant (rad)

v=±ω√x₀²​−x²

(C.1 Simple Harmonic Motion)​

Velocity in SHM

v: Velocity (m/s)

x: Displacement (m)

x₀​: Amplitude (m)

ω: Angular frequency (rad/s)

Ep​=½​mω²x²

(C.1 Simple Harmonic Motion)

Ep​: Potential energy (J)

m: Mass (kg)

ω: Angular frequency (rad/s)

x: Displacement (m)

Et=½​mω²x₀²​

(C.1 Simple Harmonic Motion)

E: Total energy (J)

m: Mass (kg)

ω: Angular frequency (rad/s)

x₀​: Amplitude (m)

v=fλ

v=λ/T

(C.2 Wave model)

v: wave speed (m/s)

λ: wavelength (m)

f: frequency (Hz)

T: time period (s)

n₁/n₂=v₁/v₂=sin⁡θ₁/sin⁡θ₂

(C.3 Wave Phenomena)

n1​,n2​: Refractive indices of media

v1,v2​: Wave velocities in media (m/s)

θ1: Angles of incidence

θ2: Angle of refraction

Constructive Interference:

Path difference = nλ

Destructive Interference: Path difference = (n+½)λ

(C.3 Wave Phenomena)

n: Integer (0, 1, 2, ...)

λ: Wavelength (m)

s=λD/d​

(C.3 Wave Phenomena)

Double slit

s: Fringe separation (m)

λ: Wavelength (m)

D: Distance to the screen (m)

d: Slit separation (m)

θ=λ​/b

(C.3 Wave Phenomena)

Single slit

θ: Angle between central max and first min (radians)

λ: Wavelength (m)

b: Width of the slit (m)

nλ=dsinθ

(C.3 Wave Phenomena)

Multiple slits

n: Order of maxima (integer)

λ: Wavelength (m)

d: Spacing between adjacent slits (m)

θ: angular separation between order of maxima (degrees or radians)

Δf​/f=λΔ/λ​≈v​/c

(C.5 Doppler Effect)

Doppler effect in light

Δf: Change in frequency (Hz)

f: Source frequency (Hz)

Δλ: Change in wavelength (m)

λ: Wavelength (m)

v: Relative velocity of source and observer (m/s)

c: Speed of the wave (m/s)

Moving Source:

f′=f×(v/v±us)​​

Moving Observer:

f′=f×(v±u)/v

(C.5 Doppler Effect)

Doppler effect in sound

f′: Observed frequency (Hz)

f: Source frequency (Hz)

v: Speed of the wave in the medium (m/s)

us​: Speed of the source relative to the medium (m/s)

u₀​: Speed of the observer relative to the medium (m/s)

v+us: Source moving away from observer

v- us: Source moving towards observer

v+u_o: observer moves TOWARD the source

v-u_o= Observer moves AWAY from the source

F=Gm₁​m₂/r²

(D.1 Gravitational fields)

Gravitational force between two bodies

F: Gravitational force (N)

G: Gravitational constant,

m₂m₁​​: Masses of the two objects (kg)

r: Distance between the centers of the masses (m)

g=F/m​=GM/r²

(D.1 Gravitational fields)

This gives the gravitational field strength at a point due to a mass M

g: Gravitational field strength

F: Gravitational force (N)

m: Mass experiencing the force

G: Gravitational constant

M: Mass creating the field (kg)

r: Distance from the center of M (m)

Ep​=−Gm₁​m₂/r

(D.1 Gravitational fields)

Gravitational potential energy

Ep​: Gravitational potential energy (J)

G: Gravitational constant

m1​,m2​: Masses of the two objects (kg)

r: Distance between the centers of the masses (m)

Vg​=−GM/r​

(D.1 Gravitational fields)

Gravitational potential

Vg​: Gravitational potential (J/kg)

G: Gravitational constant

M: Mass creating the potential (kg)

r: Distance from the center of M (m)

g=−ΔVg/​​Δr

(D.1 Gravitational fields)

Gravitational potential gradient

g: Gravitational field strength (N/kg)

ΔVg​: Change in gravitational potential (J/kg)

Δr: Change in distance (m)

W=mΔVg​

(D.1 Gravitational fields)

Work done in moving a mass

W: Work done (J)

m: Mass being moved (kg)

ΔVg​: Change in gravitational potential (J/kg)

vesc​=√(2GM​​/r)

(D.1 Gravitational fields)

The speed needed to escape the gravitational pull of a mass

vesc​: Escape velocity (m/s)

G: Gravitational constant

M: Mass being escaped from (kg)

r: Distance from the center of M (m)

vorbital=√(GM/r)

(D.1 Gravitational fields)

Obrital speed of smaller mass/speed required to maintain a stable circular orbit.

vorbital​: Orbital velocity (m/s)

G: Gravitational constant

M: Mass being orbited (kg)

r: Orbital radius (m)

F=k×(q₁q₂/r²)

(D.2 Electric and Magnetic Fields)

Electric force between two charges

F: Electric force between charges (N)

k: Coulomb's constant

q1​,q2​: Magnitudes of the charges (C)

r: Distance between the charges (m)

E=F​/q

(D.2 Electric and Magnetic Fields)

electric field strength of a charge

E: Electric field strength (N/C)

F: Electric force on the charge (N)

q: Magnitude of the charge (C)

E=V/d​

(D.2 Electric and Magnetic Fields)

Electric field strength between plates

E: Electric field strength (N/C)

V: Electric potential difference (V)

d: Separation between the plates (m)

Ep​=k×(q₁​q₂/r)

(D.2 Electric and Magnetic Fields)

potential energy

between two point charges.

Ep​: Electric potential energy (J)

k: Coulomb's constant

q1​,q2​: Magnitudes of the charges (C)

r: Distance between the charges (m)

Ve​=k×(Q/r)​

(D.2 Electric and Magnetic Fields)

calculates the electric potential at a distance r from a point charge.

Ve​: Electric potential (V)

k: Coulomb's constant

Q: Charge creating the potential (C)

r: Distance from the charge (m)

E=−ΔVe/​​Δr

(D.2 Electric and Magnetic Fields)

Electric potential gradient

E: Electric potential gradient (V/m)

ΔVe​: Change in electric potential (V)

Δr: Change in distance (m)

W=qΔVe​

(D.2 Electric and Magnetic Fields)

work done in moving a charge.

W: Work done on the charge (J)

q: Magnitude of the charge (C)

ΔVe​: Change in electric potential (V)

F=qvBsinθ

(D.3 Motion in electromagnetic fields)

magnetic force acting on a charged particle moving through a magnetic field.

F: Magnetic force on the charge (N)

q: Magnitude of the charge (C)

v: Velocity of the charge (m/s)

B: Magnetic field strength (T)

θ: Angle between v and B (degrees or radians)

F=BILsinθ

(D.3 Motion in electromagnetic fields)

The force on a current-carrying conductor in a magnetic field.

F: Magnetic force on the wire (N)

B: Magnetic field strength (T)

I: Current through the wire (A)

L: Length of the wire in the field (m)

θ: Angle between the wire and magnetic field (degrees or radians)

F/L=μ₀×(​​I₁​I₂/2πr)

(D.3 Motion in electromagnetic fields)

Force between two parallel wires carrying currents.

F: Magnetic force between two parallel current-carrying wires (N)

μ0​: Permeability of free space

I1,I2​: Currents in the two wires (A)

r: Distance between the wires (m)

L: Length of the wires (m)

E=hf

(E.1 Structure of the Atom)

E: Energy of a photon (J)

h: Planck's constant

f: Frequency of the photon (Hz)

E=mc²

(E.3 Radioactive Decay)

mass-energy equivalence

E: Energy released (J)

m: Mass lost (kg)

c: Speed of light in a vacuum

R=R₀A¹/³

(E.1 Structure of the Atom)

the radius of a nucleus

R: Radius of a nucleus (m)

R0​: Fermi radius constant

A: Mass number (number of nucleons)

En​=−13.6/n² ​eV

(E.1 Structure of the Atom)

Photon energy at a energy level

En​: Energy of an electron in the nth energy level (eV)

n: number of level (1,2,3..)

mvr=nh/2π​

(E.1 Structure of the Atom)

Angular momentum for an electron in an atom

Angular momentum: mvr

m: Mass of the electron (kg)

v: Speed of the electron (m/s)

r: Radius of the orbit (m)

n: Principal quantum number (integer): energy level or shell an electron is in around an atom

h: Planck's constant

N=N₀e (to the power of) −λt

(E.3 Radioactive Decay)

Number of undecayed nuclei

N: Number of undecayed nuclei at time t

N0: Initial number of nuclei

λ: Decay constant (s-1)

t: Time (s)

A=λN

A=λN₀ (to the power of) −λt

(E.3 Radioactive Decay)

Activity of a radioactive sample

A: Activity of the sample (Bq)

λ: Decay constant (s−1)

N: Number of undecayed nuclei

N0: Initial number of nuclei

t: Time (s)

T½=ln⁡2/λ

(E.3 Radioactive Decay)

Half-life of a sample

T½: Half-life (s)

λ: Decay constant (s−1)

Emax​=hf−Φ

(E.2 Quantum Physics)

Kinetic energy of freed electron (photoelectric effect)

Emax​: Maximum kinetic energy of emitted photoelectron (J)

h: Planck's constant (Js)

f: Frequency of incident radiation (Hz)

Φ: Work function of the material (J)

hf: Energy of photon

λ=h​/p

(E.2 Quantum Physics)

λ: De Broglie wavelength (m)

h: Planck's constant (Js)

p: Momentum of the particle (kg·m/s)

λf​−λi​=h/m​c​(1−cosθ)

The change in wavelength of a photon due to Compton scattering— when a photon collides with and transfers energy to an electron.

λf​: Final wavelength of the photon (m)

λi​: Initial wavelength (m)

h: Planck's constant (Js)

me​: Electron mass (kg)

c: Speed of light (m/s)

θ: Scattering angle (radians or degrees)

d(parsec)=1/p(arc-second)

(E.5 Fusion and Star)

The distance to a star in parsecs

d: distance to star

p: parallax angle

Φ=BAcosθ

(D.4 Induction)

Calculates Magnetic flux, or the amount of magnetic field passing through an area.

Φ: Magnetic flux (Wb)

B: Magnetic field strength (T)

A: Area perpendicular to the field (m²)

θ: Angle between the magnetic field and the normal to the surface

ε=−N×ΔΦ​/Δt

(D.4 Induction)

The induced EMF (electromotive force) in a coil of wire.

ε: Induced EMF (V)

N: Number of turns in the coil

ΔΦ: Change in magnetic flux (Wb)

Δt: Time interval (s)

ε=BvL

The induced EMF in a straight conductor moving in a magnetic field.

ε: Induced EMF (V)

B: Magnetic field strength (T)

v: Speed of the conductor (m/s)

L: Length of conductor within the field (m)

τ=Frsinθ

(A.4 Rigid Body Mechanics)

The torque applied by a force around a pivot point.

τ: Torque (N·m)

F: Applied force (N)

r: Distance from axis to point of force application (m)

θ: Angle between force and lever arm

Δθ=((ωf​+ωi)/2)×​​t

ωf​=ωi​+αt

Δθ=ωi×t+½αt²

ωf²​=ωi²+2αΔθ

Angular version of SUVAT equations

(A.4 Rigid Body Mechanics)

Δθ: Angular displacement (rad)

ωi: Initial angular velocity (rad/s)

ωf​: Final angular velocity (rad/s)

α: Angular acceleration (rad/s²)

t: Time (s)

I=∑mr²

(A.4 Rigid Body Mechanics)

Moment of inertia

I: Moment of inertia (kg·m²)

m: Mass of each particle (kg)

r: Distance from rotation axis (m)

τ=Iα

(A.4 Rigid Body Mechanics)

Torque required to produce angular acceleration.

τ: Torque (N·m)

I: Moment of inertia (kg·m²)

α: Angular acceleration (rad/s²)

L=Iω

(A.4 Rigid Body Mechanics)

Angular momentum of a rotating body.

L: Angular momentum (kg·m²/s)

I: Moment of inertia (kg·m²)

ω: Angular velocity (rad/s)

ΔL=τΔt

(A.4 Rigid Body Mechanics)

Angular impulse

τ: Torque (N·m)

ΔL: Change in angular momentum (kg·m²/s)

Δt: Time interval (s)