IB Physics equations NOT in formula booklet

acceleration formula

velocity formula

a=v/t

v=s/t

Centripetal force formula

F=mv²/r=mrω²

Translational and rotational relationship

s=r0

v=rw

a=ra

time of emission (A.5 Relativity)

t emission=t observation- travel time

power

P=E/t, P=Q/t

emissivity

P=eσAT⁴

• P = power emitted (W)

• ϵ = emissivity (no unit, just a number)

• σ = Stefan–Boltzmann constant

• A = surface area (m²)

• T = temperature in Kelvin (K)

Intensity

I=Power/Area

I=Solar constant/4

I=σT⁴

equation for n using molar mass

n=mass/molar mass

velocity of particles in a gas

V total= Number of particles× V one particle

Kinetic energy of particles in a gas

Ek=(3/2)K_BT

Shows Ek only depends on temperature

You can also use the Ek equation found in A.3

km/h to m/s

Multiple given value by 5/18

rpm to w(rad/s)

rpm×(2π/60)

Power for object at constant speed vs. accelerating

P_{constant speed}=F_resistiveV

P_accelerating=F_{(resistive+ma)}V

Energy density formula

e= energy released/m³

Binding Energy Per Nucleon

Binding Energy per nucleon=Eb​/A

Eb​: binding energy, A: mass number.

Restoring force in simple pendulum

F=-mgsinθ

Acceleration in simple pendulum

a=-gsinθ=-g(x/L)

• a: acceleration

• g: gravity

• x: displacement from equilibrium

• L: length of pendulum

Refrective index

n=c/v

c= speed of light

v: speed of light in medium

Critical angle

sinθ= n2/n1

Max Velocity in SHM

Vmax= ωx₀

Number of secondary maxima

N°of slits-2

Relationship of intensity with number of slits

I ∞(N°of slits)²

How to calculate slit separation

lines per mm

lines per m

m per line (reciprocal)

Kinetic energy of a SHM wave

Ek= Et- Ep

Wavelength of nth hamonic of string

λ= 2L/n

L: Length of string (m)

n: interger number greater than zero (1,2,3...)

Wavelength of nth harmonic on pipe

λ= 4L/n

L: Length of string (m)

n: interger number greater than zero (1,2,3...)

* ONLY ODD HARMONIC CAN EXIST UNDER PIPE THAT IS OPEN AT ONE END

Natural frequency

fn= nv/2L

L: Length of string/pipe (m)

n: interger number greater than zero (1,2,3...)

v: speed of wave

Electric field strength equation

E=kq/r²

Radius of the path of a charged particle in a perpendicular magnetic field

r= mv/BQ

Photon energy

E=hc/λ

Mechanical energy

E_T = E_k + E_p

E_T = E_k + E_gp + E_h

Fraction of sample remaining after radioactive decay

(1/2)ⁿ

n= number of half lives

Work done in moving a object a certain distance away from the mass

(D.1 Gravitational fields)

W=∆E_m

W=∆E_p+E_k

E_k= q∆V_e

W= -GMm/2r

Electric potential (second version)

V_e= E_p / q

Flux Linkage

total magnetic flux passing through a coil

Flux Linkage= NΦ

Induced E.M.F for Coil Moving through a field

E=NBvL

Observed Wavelength in Doppler effect of light

λ’ = velocity of wave/ observed frequency

Threshold frequency for photoelectric effect

ϕ=hf_o

ϕ: Work Function (J)

h: Plancks constant

f_o: Threshold frequency (Hz)

Energy gained or lost by an electron when it is accelerated through a potential difference (V)

E=e V

E_max= e V_o

Where V_o is the stopping potential

Activity of nuclei after some time

A=A_oe^-λt

Where

A_o is the initial activity

λ is the decay constant

t: time

Energy released after decay

E_released=BE_products-BE_{original atom}

BE: Binding energy

(or other way around)

Half life

t_1/2= total time elapsed / number of half lives

Activity of nuclei using half life

A=A_o × 2^-t/t_1/2

t_1/2 is the half-life

t is the time elapsed.

Specific energy

energy per unit mass of a substance

SE= Fission energy released/ mass

Mass of an atom (Fission)

m= Energy input / Specific energy

horizontal vector component of a projectile

a projectile’s part of its velocity that acts along the horizontal (x) axis

v_x=vcosθ

When it's used:

• To calculate how far the projectile travels horizontally (range).

• To find the horizontal displacement at any time, using x=v_xt

• Since there’s no horizontal acceleration (ignoring air resistance), v_x stays constant during flight.

vertical component of a projectile

a projectile is the part of its velocity that acts along the vertical (y) axis.

v_y=vsinθ

When it's used:

• To calculate how high the projectile goes (maximum height).

• To find vertical motion at any time

Terminal velocity

F_drag=mg

Work-Energy Transferred Theorem

The work done on an object is equal to the change in its energy (usually kinetic energy)

W=ΔE

Two dimensional collisions and explosions

Conservation of momentum in the x-direction:

m₁v_1icosθ₁ +m₂v_2icosθ₂ = m₁v_1fcosθ’₁+m₂v_2fcosθ'₂

Conservation of momentum in the y-direction:

m₁v_1isinθ₁ +m₂v_2isinθ₂ = m₁v_1fsinθ’₁+m₂v_2fsinθ'₂

• m1,m2 = masses of the objects

• v1i,v2= initial velocities of the objects

• v1f,v2f= final velocities of the objects

• θ1,θ2 = angles of the initial velocities

• θ1′,θ2′​ = angles of the final velocities

average angular velocity

ω_avg​=Δθ/Δt​

• ωavg​ = average angular velocity (in radians per second, rad/s)

• Δθ = change in angular displacement (in radians)

• Δt= time interval during which the change in angular displacement occurs

Moment of Inertia for Solid Cylinder or Disk

I=(1/2)mr²

Rotational equilibrium

τ_clockwise=τ_{counter-clockwise}

∑τ=0

Total energy in rotational motion

E_T= E_k + E_kR

Average Speed of Gas Molecules

v_rms​=√3kB​T​​/√m

• v_rms=speed of the gas molecules

• kB= Boltzmann constant

• T = temperature of the gas (in Kelvin, K)

• m = mass of one gas molecule (in kilograms, kg)

The Stefan-Boltzmann constant (σ), the universal gas constant (R), and Avogadro’s number (N_A​) are linked by the equation

k_B​=​R​/N_A

• kB​ is the Boltzmann constant

• R is the universal gas constant

• NA is Avogadro’s number

Intensity of electromagnetic radiation at a distance r from a source with power

I=P/4πr²

• I = intensity (in watts per square meter, W/m²)

• P = power of the source (in watts, W)

• r = distance from the source (in meters, m)

• 4πr²= surface area of a sphere

Uses:

• Calculate how the intensity of sound or light decreases with distance from a point source

• Calculating the intensity of radiation coming from stars or other celestial objects as it moves through space.

Maximum and minimum values for an emf in an ac generator

ε​=±BANω

ε_min​=0

ε(t)=ε_max​sin(ωt)

• B = magnetic field strength (in tesla, T)

• A= area of the coil (in square meters, m²)

• ω = angular velocity (in radians per second, rad/s)

• N = number of turns in the coil (dimensionless)

positive and negative signs (±) indicate that the direction of the induced emf alternates

Potential divider equation

V_X= (R_x/R_total) × V_total

• V_X​ is the voltage across the component RXR_XRX​ (the component you are interested in),

• V_total is the total voltage across the series circuit (usually the emf of the source),

• R_X​ is the resistance of the component you want the voltage across,

• R_total​ is the total resistance of the circuit.

emf equation

E=W(energy supplied)/Q

V= E- Ir

Cross sectional area of a circle

A=πr², where r is the radius of the circle.

surface area of a sphere

A=4πr²

power equation for rotational motion

P=τ⋅ω

Rotational Work

W=τ⋅θ

Maximum order seen in a difraction pattern

n_max=d/wavelength