Angular Momentum Calculator
Calculate angular momentum using L = I·ω for rigid bodies or L = m·v·r for point masses.
How it works
- 1Choose a method: “Rigid body (L = I·ω)” for a spinning object with a known moment of inertia, or “Point mass (L = m·v·r)” for a particle on a circular path.
- 2Enter the inputs — for rigid body: I (kg·m²) and ω (rad/s); for point mass: mass, velocity, and radius with metric or imperial units.
- 3The calculator returns angular momentum in kg·m²/s. It is conserved when no net external torque acts.
Use cases
- Orbital mechanics — the angular momentum of a planet or satellite via L = m·v·r.
- Mechanical engineering — flywheels, gyroscopes, and rotating machinery via L = I·ω.
- Biomechanics — why a skater spins faster when pulling their arms in (smaller I, larger ω).
Frequently asked questions
What is the formula for angular momentum?
Two forms: for a rigid body about a fixed axis, L = I·ω (I in kg·m², ω in rad/s); for a point mass on a circular path, L = m·v·r (m in kg, v in m/s, r in m). Both give kg·m²/s.
Why is angular momentum conserved?
It is conserved when no net external torque acts (τ = dL ÷ dt). A figure skater who pulls their arms in lowers their moment of inertia I; since L = I·ω is constant, ω rises and they spin faster.
Can you show a worked example?
Point mass: a 2 kg ball at 10 m/s on radius 5 m → L = 2 × 10 × 5 = 100 kg·m²/s. Rigid body: a flywheel with I = 4 kg·m² at ω = 25 rad/s → L = 4 × 25 = 100 kg·m²/s.
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