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Angular Momentum Calculator

Find the angular momentum of an orbiting or rotating point mass with L = m·v·r — or solve for mass, velocity or radius. Choose your own units for each input.

 

Formula

$$ L = m\,v\,r \qquad m=\frac{L}{vr} \qquad v=\frac{L}{mr} \qquad r=\frac{L}{mv} $$

Worked example

A 2 kg mass moving at 10 m/s at radius 25 m has \( L = (2)(10)(25) = 500\ \text{kg·m}^2/\text{s} \).

How it works

Angular momentum measures the rotational motion of a mass about a point. For a point mass it is L = m v r — mass times its speed times its distance from the axis (for velocity perpendicular to the radius).

Angular momentum is conserved when no external torque acts, which is why a spinning skater speeds up as they pull their arms in (smaller r means larger v) and why planets sweep out equal areas in equal times.

Frequently asked questions

What is the formula for angular momentum?

For a point mass, L = mvr — mass times velocity times radius. For an extended rotating body it is L = Iω, the moment of inertia times angular velocity.

What are the units of angular momentum?

Kilogram metres squared per second (kg·m²/s), equivalent to joule-seconds (J·s).

Why is angular momentum conserved?

In the absence of an external torque, total angular momentum stays constant. This is why a skater spins faster when pulling their arms in — reducing r increases v to keep L fixed.

How is angular momentum different from linear momentum?

Linear momentum (p = mv) describes straight-line motion; angular momentum (L = mvr) describes rotation about a point and additionally depends on the distance from the axis.

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