Calculates angular momentum, the rotational counterpart to linear momentum, from an object’s moment of inertia and angular velocity.
How it works
Moment of inertia is multiplied directly by angular velocity to give angular momentum.
What this does not include
This does not include computing the moment of inertia itself for a specific shape — that value must be supplied as an input.
How to use this calculator
- Enter the moment of inertia and the angular velocity.
A worked example
A moment of inertia of 2 kg·m² spinning at 3 rad/s → angular momentum = 2 × 3 = 6 kg·m²/s.
A moment of inertia of 0.5 kg·m² spinning at 10 rad/s → 5 kg·m²/s.
What the variables mean
| Variable | Meaning |
|---|---|
| Moment of inertia | Resistance to changes in rotation, based on mass distribution |
| Angular velocity | Rotational speed, in radians per second |
Edge cases worth knowing
Angular momentum is conserved in a closed system — a figure skater pulling their arms in reduces their moment of inertia, and their angular velocity increases to keep the product constant, which is why they spin faster.
A missing moment of inertia makes the calculation impossible — it depends on the object’s actual mass distribution, which isn’t a value this calculator can assume.
Frequently asked questions
Why does a figure skater spin faster when pulling their arms in?
Pulling arms in reduces moment of inertia, and since angular momentum is conserved (stays constant) without an external torque, angular velocity must increase to compensate.
What’s the linear-motion equivalent of angular momentum?
Linear momentum (mass times velocity) — angular momentum plays the same role for rotation that linear momentum plays for straight-line motion.
What are the units of angular momentum?
Kilogram-meters-squared per second (kg·m²/s) in SI units.
