Angular Momentum Calculator
angular momentum calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Angular Momentum Calculator
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Formula: L = Iω or L = mvr
Worked example — 10 kg·m²/s
Formula
L = Iω or L = mvr
Rotational analog of linear momentum. Conserved in the absence of external torques.
Worked Examples
Example 1: Spinning wheel
Problem:I=2 kg·m², ω=5 rad/s
Solution:L=2×5=10 kg·m²/s
Result:10 kg·m²/s
Frequently Asked Questions
What is angular momentum?
Angular momentum (L) is the rotational equivalent of linear momentum. For a rigid body, L = Iω, where I is the moment of inertia (kg·m²) and ω is the angular velocity (rad/s). Its SI unit is kg·m²/s.
How do you calculate angular momentum?
Use L = Iω for rotating bodies, or L = mvr for a point mass moving in a circle. For example, a wheel with I = 2 kg·m² spinning at ω = 5 rad/s has L = 2 × 5 = 10 kg·m²/s.
What units does angular momentum use?
The SI unit of angular momentum is kg·m²/s, equivalent to J·s (joule-seconds). The moment of inertia is in kg·m² and angular velocity in rad/s, giving kg·m²/s when multiplied.
When is angular momentum conserved?
Angular momentum is conserved when no net external torque acts on the system. A classic example: an ice skater spinning at 2 rev/s with arms extended halves their moment of inertia by pulling arms in, instantly doubling their spin rate to 4 rev/s.
What is momentum and how is it conserved?
Momentum is p = mv (mass times velocity). In a closed system with no external forces, total momentum is conserved. In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, momentum is conserved but kinetic energy is not. Impulse (F*t) equals the change in momentum.
Background & Theory
Angular Momentum Conservation in Practice
Angular momentum L = Iω is conserved whenever no external torque acts on a system — this is the rotational twin of linear momentum conservation, and it explains several everyday phenomena that look almost magical until you see the math.
| Example | What changes | Why |
|---|---|---|
| Figure skater pulling in arms | Spin rate roughly doubles | I drops as mass moves closer to the axis; L stays fixed so ω rises |
| Diver tucking mid-air | Faster somersault rotation | Same principle — smaller I, larger ω, same L |
| Collapsing star → pulsar | Rotation speeds up to hundreds of times per second | Stellar radius shrinks by orders of magnitude, I falls dramatically |
| Flywheel energy storage | Stores KE = ½Iω² for later release | High ω is favored since energy scales with ω² but L only scales with ω |
Note that rotational kinetic energy and angular momentum scale differently with speed (ω² versus ω), which is why the skater's kinetic energy actually increases when they pull their arms in — that extra energy comes from the muscular work done pulling the arms inward against the outward "centrifugal" tendency.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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