Change in Angular Momentum Calculator

Calculator

Large screens show three columns, medium shows two, and mobile shows one.

Method

Initial ω (ω1)

Used for inertia method only.

Final ω (ω2)

Used for inertia method only.

Initial inertia source

I1 (moment of inertia)

Compute I1 from shape

Shape

Mass

Radius

Rod length

Uses standard inertias: disk (1/2mr^2), hoop (mr^2), sphere (2/5mr^2), shell (2/3mr^2), rod center (1/12 mL^2), rod end (1/3 mL^2).

Final inertia source

I2 (moment of inertia)

Compute I2 from shape

Shape

Mass

Radius

Rod length

Select rod shapes to use length; other shapes use radius.

L1 (initial)

L2 (final)

Tip: If your values are in N·m·s, enter them as-is.

Average torque (τ)

Time interval (Δt)

This method returns ΔL directly as angular impulse.

Formula used

L = Iω where L is angular momentum, I is moment of inertia, and ω is angular velocity.
ΔL = L2 − L1 gives the change between final and initial states.
ΔL = ∫ τ dt; for constant or average torque, ΔL = τ_avg × Δt.

Units: kg·m²/s is numerically equal to N·m·s.

How to use this calculator

Example data table

Scenario	Inputs	Computed L1	Computed L2	ΔL
Inertia + speed	I1=0.12 kg·m², ω1=30 rad/s; I2=0.18 kg·m², ω2=45 rad/s	3.600 kg·m²/s	8.100 kg·m²/s	4.500 kg·m²/s
Torque + time	τ=12.5 N·m; Δt=0.8 s	0.000 kg·m²/s	10.000 kg·m²/s	10.000 kg·m²/s
Direct values	L1=6.2; L2=4.9 (kg·m²/s)	6.200 kg·m²/s	4.900 kg·m²/s	-1.300 kg·m²/s

These examples illustrate sign, units, and method differences.