IB Physics HL formulas

A.4 Rigid Body Mechanics (HL) : τ = Fr sinθ

τ: torque
F: force
r: distance from axis to point of action of F
θ: angle between direction of F and direction of r

A.4 Rigid Body Mechanics (HL) : rigid body mechanics (ω_f² = ω_i² + 2α∆θ)

Δθ: angular displacement

ω_f: final angular velocity

ω_i: initial angular velocity

a: angular acceleration

t: time
(use + and - to include direction )

A.4 Rigid Body Mechanics (HL) : I = Σmr²

I: moment of inertia
m: mass
r: distance from point or axis of rotation

(Note: Σ means sum)

A.4 Rigid Body Mechanics (HL) : τ = Iα

τ: resultant/net torque

I: moment of inertia
a: angular acceleration

A.4 Rigid Body Mechanics (HL) : L = Iω

L: angular momentum

I: moment of inertia

ω: angular velocity

A.4 Rigid Body Mechanics (HL) : ∆L = τ∆t

ΔL: change in angular momentum

τ: resultant/net torque
Δt: time taken

A.4 Rigid Body Mechanics (HL) : ∆L = ∆(Iω)

ΔL: change in angular momentum

I: moment of inertia
ω: angular velocity

A.4 Rigid Body Mechanics (HL) : E_k = (1/2) Iω² = L² / 2I

E_k: rotational kinetic energy

I: moment of inertia
ω: angular speed
L: angular momentum

A.5 Galilean and special relativity (HL) : x ' = x − vt

• x′: position in the moving frame

• x: position in the original (stationary) frame

• v: speed of the moving frame (relative to the original)

• t: time in the original frame

A.5 Galilean and special relativity (HL) : t' = t

• t: time in the original frame

• t′ = time in the moving frame (traveling at speed v relative to the original)

A.5 Galilean and special relativity (HL) : u' = u−v

u’: velocity of body in an inertial frame of reference

v: relative speed between the two inertial frames

u: velocity of the same body in the original frame of reference

A.5 Galilean and special relativity (HL) : x' = γ(x−vt)

• x′: position in the moving frame

• x: position in the original (stationary) frame

• v: speed of the moving frame (relative to the original)

• t: time in the original frame

• γ: the Lorrentz factor

A.5 Galilean and special relativity (HL) : γ = 1 / √1- (v²/c²)

• γ: the Lorrentz factor

• v: speed of the moving frame (relative to the original)

• c: speed of light in vacuum (constant)

A.5 Galilean and special relativity (HL) : t ' = γ (t − (vx / c²) )

• γ: the Lorrentz factor

• v: speed of the moving frame (relative to the original)

• c: speed of light in vacuum (constant)

• t: time in the original frame

• x: position in the original (stationary) frame

• t′ = time in the moving frame (traveling at speed v relative to the original)

A.5 Galilean and special relativity (HL) : u' = (u−v) / 1− (uv/c²)

u’: velocity of body in an inertial frame of reference

v: relative speed between the two inertial frames

u: velocity of the same body in the original frame of reference

c: speed of light in vacuum (constant)

A.5 Galilean and special relativity (HL) : (∆s)² = (c∆t)² − ∆x²

Δs: space-time interval between two events
c: speed of light
Δt: time interval

Δx: distance between the events

A.5 Galilean and special relativity (HL) : ∆t = γ∆t₀

Δt: time interval between two observed events (2 different clocks)

γ: the Lorrentz factor
Δt₀: proper time (time interval measured by same clock)

A.5 Galilean and special relativity (HL) : L = L₀ / γ

L: observed length

L₀: proper length
γ: the Lorrentz factor

A.5 Galilean and special relativity (HL) : tanθ = v/c

θ: angle of worldline from the vertical axis in a space-time diagram

v: speed of the body

c: speed of light

B.1 Thermal energy transfers : ρ = m/V

ρ: density

m: mass

V: volume

B.1 Thermal energy transfers : E_k = (3/2)k_BT

E_{k: average kinetic energy of a gas}

k_B: Boltzmann constant

T: absolute temperature

B.1 Thermal energy transfers : Q = mc∆T

Q: heat energy transferred (J)

m: mass
c: specific heat capacity

ΔΤ: change in temperature

B.1 Thermal energy transfers : Q = mL

Q: heat energy transferred (J)

m: mass
L: specific latent heat

B.1 Thermal energy transfers : p = (mc∆T) / t

t: time

m: mass
c: specific heat capacity

ΔΤ: change in temperature

B.1 Thermal energy transfers : ∆Q / ∆T = kA (∆t / ∆x)

Power (∆Q / ∆T)

ΔQ: amount of heat (energy) transfer
Δt: time taken
k: thermal conductivity of material
A: surface area of the surface that emits heat
ΔT: temperature difference between hot and cold sides

Δx: thickness (distance between hot and cold sides)

B.1 Thermal energy transfers : L = σ AT⁴

Stars (luminosity)

L: luminosity (total power output)

σ: Steffan-Boltzmann constant

A: surface area of body
T: temperature

B.1 Thermal energy transfers : b = L / 4πd²

Stars (brightness)

b: brightness (intensity)
L: luminosity
d: distance from the source

B.1 Thermal energy transfers : λ_maxT = 2.9 ×10^-3mK

λ_max: peak wavelength

T: temperature

B.2 Greenhouse effect : emissivity = power radiated per unit area / σT⁴

σ: Steffan-Boltzmann constant

T : temperature

power radiated per unit area: Intensity

Black Body emissivity = 0

B.3 Gas Laws: P = F/A

P: pressure

F: force
A: area

B.3 Gas Laws : n = N / N_A

n: number of moles
N: number of particles (atoms or molecules)

N_A: Avogadro constant

B.3 Gas Laws : PV / T = constant

P: pressure
V: volume
T: temperature

B.3 Gas Laws : PV = nRT = Nk_B T

Ideal Gas Law

P: pressure
V: volume
T: temperature

n:number of moles
R: gas constant
N: number of particles

K_B: Boltzmann constant

B.3 Gas Laws : P = (1/3) ρ v²

P: pressure
ρ: density of gas
v: root mean square speed of particles (r.m.s speed)

B.3 Gas Laws : U = (3/2) nRT = (3/2) Nk_B T

Internal Energy

T: temperature

n: number of moles
R: gas constant
N: number of particles

K_B: Boltzmann constant

U: internal energy of gas

B.5 Current and circuits : I = ∆q / ∆t

Electric Current

I: current
Δq: amount of charge passing through a surface

Δt: time taken

B.5 Current and circuits : V = W / q

V: potential difference

W: work done
q: charge

B.5 Current and circuits : R = V / I

R: resistance
V: potential difference

I: current

B.5 Current and circuits : ρ = RA / L

Resistivity

ρ: resistivity
R: resistance
A: cross-sectional area

L: length

B.5 Current and circuits : P = IV

= I²R

= V² / R

P: power
I: current
V: potential difference

R: resistance

B.5 Current and circuits : ε = I (R+r)

ε: electromotive force (emf)
I: current
R: resistance of connected circuit (external)

r: internal resistance (internal)

B.4 Thermodynamics (HL) : Q = ∆U +W

1st Law of Thermodynamics

Q: amount of thermal energy (heat) transferred into the system

ΔU: change in internal energy
W: work done by the gas on surroundings (area under the curve)

B.4 Thermodynamics (HL) : W =P∆V

W: work done by gas on surroundings (area under the curve)

P: pressure
ΔV: change in volume

B.4 Thermodynamics (HL) : ∆U = (3/2) nR∆T

= (3/2) Nk_B ∆T

ΔU: change in internal energy of a gas

n: number of moles
R: Gas constant
ΔΤ: change in temperature

N: number of atoms

k_B: Boltzmann constant

B.4 Thermodynamics (HL) : ∆S = ∆Q / T

ΔS: change in entropy
ΔQ: amount of thermal energy (heat) that flows into a body

T: temperature

B.4 Thermodynamics (HL) : S = k_B lnΩ

S: entropy
k_B: Boltzmann constant
Ω: number of possible micro states of the system

B.4 Thermodynamics (HL) : PV^5/3 = constant

the relationship between P + V for an ideal gas under adiabatic conditions

P: Pressure of monatomic ideal gas

V: Volume of monatomic ideal gas

B.4 Thermodynamics (HL) : η = useful work / input energy

η: efficiency

B.4 Thermodynamics (HL) : η_carnot = 1− (T_c / T_h)

η_carnot: efficiency of a Carnot cycle

T_c: temperature of cold gas
T_h: temperature of hot gas

C.1 Simple harmonic motion : a = −ω² x

a: acceleration
ω: angular frequency
×: displacement from equilibrium position

C.1 Simple harmonic motion : T = 1 / f

= 2π / ω

Τ: period
f : frequency
ω: angular frequency (2π/T)

C.1 Simple harmonic motion : T = 2π √m / k

T: period of a mass-spring system

m: mass
k: spring constant

C.1 Simple harmonic motion : T = 2π √l / g

T: period of simple pendulum
l: length
g: 9.81 m/s²

C.2 Wave model : v = f λ

= λ / T

v: wave speed

f : frequency

λ: wavelength

C.3 Wave phenomena : n₁ / n₂ = sinθ₂ / sinθ₁

= v₂ / v₁

Snell’s Law

n₁: refractive index of medium 1

n₂: refractive index of medium 2 (bigger n)

θ₁: angle of incidence
θ₂: angle of refraction

v₁: speed of wave in medium 1

v₂: speed of wave in medium 2

C.3 Wave Phenomena : Constructive Interference nλ

Waves line up (crests and troughs match)

n= 0, 1, 2, 3, ...

λ: wavelength

C.3 Wave Phenomena : Destructive Interference (n + (1/2) ) λ

Waves are out of phase (crests hit troughs)

n= 0, 1, 2, 3, ...

λ: wavelength

C.3 Wave phenomena : s = λD / d

s: distance between adjacent maxima

λ: wavelength
D: distance between slits and screen

d: distance between slits

C.5 Doppler Effect: ∆f / f = ∆λ / λ

≈ v / c

Δf : change/shift in frequency
f : frequency of emitted wave
Δλ: change/shift in wavelength
λ: wavelength of emitted wave
v: relative speed between source and observer

c: speed of light (constant)

C.1 Simple harmonic motion (HL) : x = x₀ sin(ωt + φ)

x: displacement from equilibrium position

x₀: amplitude
ω: angular frequency
t: time

φ: initial phase

C.1 Simple harmonic motion (HL) : v = ωx₀ cos(ωt + φ)

x₀: amplitude
ω: angular frequency
t: time

φ: initial phase
v: velocity

C.1 Simple harmonic motion (HL) : v = ±ω √ (x₀² − x²⁾

x: displacement from equilibrium position

x₀: amplitude
ω: angular frequency
v: velocity

C.1 Simple harmonic motion (HL) : E_T = (1/2) m ω² x₀²

m: mass

E_T: total energy of simple harmonic oscillator
ω: angular frequency
x₀: amplitude

C.1 Simple harmonic motion (HL) : E_P = (1/2) m ω² x²

E_P: potential energy of simple harmonic oscillator

x: displacement from equilibrium position

ω: angular frequency
m: mass

C.3 Wave phenomena (HL) : θ =λ / b

θ: angle at which first diffraction minimum appears

λ: wavelength
b: slit width

C.3 Wave phenomena (HL) : nλ = d sinθ

n: order (1, 2, 3, ... )
λ: wavelength
d: distance between slits of diffraction grating
θ: angle at which this order minimum will appear

Condition for Constructive Interference

C.5 Doppler effect (HL) : f ′ = f (v / v±u_s ) Moving source

f ́: observed frequency

f : emitted frequency

v: wave speed

u_s: speed of source

C.5 Doppler effect (HL) : f ′ = f ( v±u_o / v ) Moving observer

u_o: speed of observer

f ́: observed frequency

f : emitted frequency

v: wave speed

D.1 Gravitational fields : F = G ( m₁m₂ / r² )

Gravitational force between two masses

F: gravitational force
G: gravitational constant
m₁: mass of body 1
m₂: mass of body 2
r: distance between the centres of the 2 bodies

D.1 Gravitational fields: g = F / m

= GM / r²

G: gravitational field strength

F: gravitational force
m: mass
g: gravitational constant

M: mass of the body that creates the gravitational field

r: distance from the centre of that body

D.2 Electric and magnetic fields : F = k ( q₁ q₂ / r² )

where k = 1 / 4πε₀

F: electric field force between two charged particles

k: Coulomb’s constant
ε₀: permittivity of a vacuum (constant)
q₁: charge of particle 1

q₂: charge of particle 2

D.2 Electric and magnetic fields : E = F / q

E: electric field strength

F: electric field force

q: charge

D.2 Electric and magnetic fields : E = V / d

Parallel Plates

E: electric field strength of a uniform electric field
V: potential difference between two points (or metal plates)

d: distance between the two points (or metal plates)

D.3 Motion in electromagnetic fields : F =qvBsinθ

Right-Hand Rule

F: magnetic force on moving charged particle

q: charge of particle
v: speed of particle
B: magnetic field strength

θ: angle between magnetic field lines and direction of speed

D.3 Motion in electromagnetic fields : F =BILsinθ

F: magnetic force on current currying wire

B: magnetic field strength
I: current
L: length of wire in the magnetic field

θ: angle between magnetic field lines and current

D.3 Motion in electromagnetic fields : F / L = μ_{0 (} I₁I₂ / 2πr )

F: magnetic force between current currying wire

L: length of wire
μ₀: permeability of free space (constant)
I₁: current in wire 1

I₂: current in wire 2
r: distance between wires

D.1 Gravitational fields (HL) : E_P = -G ( m₁m₂ / r )

Gravitational Potential Energy between two masses

E_P: gravitational potential energy

G: gravitational constant
m₁: mass of body 1
m₂: mass of body 2

r: distance between the centres of bodies

D.1 Gravitational fields (HL) : V_g = −G M / r

V_g: gravitational potential at a point in a gravitational field

G: gravitational constant
M: mass of the body creating the field
r: distance of the point from the centre of the body.

D.1 Gravitational fields (HL) : g = − (∆V_g / ∆r )

g: gravitational field strength
ΔV_g: change in the gravitational potential between two points

Δr: distance between the two points

D.1 Gravitational fields (HL) : W = m∆V_g

W: work done to move a mass in a gravitational field
m: mass of body that is moving
ΔV_g: change in the gravitational potential between two points

D.1 Gravitational fields (HL) : V_esc = √2GM / r

Escape Velocity

v_esc: speed needed to escape a gravitational field

G: gravitational constant
M: mass of body creating the gravitational field

r: distance from the centre of that body

D.1 Gravitational fields (HL) : V_orbital = √GM / r

Orbital Velocity

v_orbital: orbital speed
G: gravitational constant
M: mass of body creating the gravitational field

r: distance from the centre of that body

D.2 Electric and magnetic fields (HL) : E_P = k ( q₁q₂ / r )

E_P: electric potential energy

k: Coulomb’s constant
q₁: charge on body 1
q₂: charge on body 2

r: distance between the centres of the bodies

D.2 Electric and magnetic fields (HL) : V_e = kQ / r

V_e: electric potential at a point in an electric field

k: Coulomb’s constant
Q: charge creating the field
r: distance between point and centre of charge

D.2 Electric and magnetic fields (HL) : E = − ( ∆V_e / ∆r )

E: electric field strength
ΔV: electric potential difference between two points in the field

Δr: distance between the points

D.2 Electric and magnetic fields (HL) : W =q∆ V_e

W: work done to move a charge in an electric field

q: charge moved
ΔV_e: electric potential difference between the points

D.4 Induction (HL) : Φ = BAcosθ

Φ: magnetic flux (weber)
B: magnetic field strength (tesla)
A: area
θ: angle between magnetic field lines and the perpendicular direction to the surface

D.4 Induction (HL) : ε = −N ( ∆Φ / ∆t )

ε: induced emf
N: number of loops on coil

ΔΦ: change in magnetic flux

Δt: time taken

D.4 Induction (HL) : ε = BvL

ε: emf induced across the ends of a straight conductor moving in a magnetic field

B: magnetic field strength
v: speed of conductor
l: length of conductor in field

E.1 Structure of the atom : E = hf

E: energy of a photon (J)

h: Planck’s constant
f : frequency

E.3 Radioactive decay : E = mc²

E: energy released (J)
m: mass ‘loss’ (change in mass)

c: speed of light (constant)

E.5 Fusion and stars : d(parsec) = 1 / p(arc-second)

d: distance to star

p: parallax angle

E.1 Structure of the atom (HL) : R = R₀ A^1/3

R: radius of atom
R₀: Fermi radius (constant)
A: atomic number (number of protons)

E.1 Structure of the atom (HL) : E = − (13.6 / n²⁾ eV

E: energy value of energy level
n: quantum number of energy level (n= 1,2,3,..)

(eV is just the unit, energy here is calculated in electrovolts)

E.1 Structure of the atom (HL) : mvr = nh / 2π

mvr: angular momentum
m: mass
v: linear speed
r: radius of circular path
n: quantum number (n=1,2,3,4,...)

h: Planck’s constant

E.2 Quantum physics (HL) : E_max = hf − Φ

E_max: maximum kinetic of energy of emitted electrons

h: Planck’s constant
f: frequency of incident radiation
Φ: work function of metal surface

E.2 Quantum physics (HL) : λ = h / p

λ: wavelength of a particle

h: Planck's constant

p: momentum of the particle

E.2 Quantum physics (HL) : λ_f −λ_i =∆λ

= (h / m_ec ) (1−cosθ)

λ_f: final wavelength
λ_i: initial wavelength
Δλ: change in wavelength
h: Planck’s constant
m_e: mass of electron (constant)
c: speed of light in vacuum (constant)

θ: scattering angle

E.3 Radioactive decay (HL) : N = N₀ e^{^}-λt

N: number of nuclei left after time t
N₀: original number of nuclei in the sample (at t=0)

λ: decay constant of material
t: time

E.3 Radioactive decay (HL) : A = λN

= λN₀ e^{^}-λt

N: number of nuclei left after time t
N₀: original number of nuclei in the sample (at t=0)

λ: decay constant of material
t: time
A: activity (number of decays per second)