Angular Momentum Calculator
Find angular momentum for a spinning rigid body (L = I·ω) or a particle moving around a point (L = m·v·r).
How it works
Rigid body: L = I·ω · Point particle: L = m·v·r
Angular momentum is the rotational counterpart of linear momentum. For a rigid body it is L = I·ω, the product of the moment of inertia and the angular velocity; for a particle circling a point it is L = m·v·r. In the absence of an external torque it is conserved, which is why a spinning skater speeds up as they pull their arms in — reducing I forces ω to rise so that L stays constant.
Worked example
A flywheel with I = 0.5 kg·m² spinning at ω = 10 rad/s has L = 0.5 × 10 = 5 kg·m²/s and rotational energy ½ × 0.5 × 10² = 25 J. A 1 kg ball moving at 5 m/s in a circle of radius 2 m has L = 1 × 5 × 2 = 10 kg·m²/s.
Sources: Angular momentum — Wikipedia
Frequently asked questions
When is angular momentum conserved?
Whenever the net external torque on a system is zero. Then L stays constant even if the shape changes — the classic example is a figure skater spinning faster as they draw their arms inward and lower their moment of inertia.
What are the units of angular momentum?
Kilogram-metre-squared per second (kg·m²/s), which is the same as a joule-second (J·s). Both L = I·ω and L = m·v·r give these units.
How does angular momentum relate to torque?
Torque is the rate of change of angular momentum: τ = ΔL/Δt. A constant torque changes L steadily, just as a force changes linear momentum.
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This calculator is for educational purposes. Double-check important results before acting on them.