Angular Momentum Calculator

What Is Angular Momentum?

Angular momentum quantifies the rotational motion of a body. A spinning figure skater, a gyroscope, and an orbiting planet all carry angular momentum. In the absence of external torque, total angular momentum stays constant.

Angular Momentum Formula

$$ L = I \omega $$

$I$ is the moment of inertia in kg·m$^2$ and $\omega$ is angular velocity in rad/s. The SI unit of angular momentum is kg·m$^2$/s, equivalent to joule-seconds for rotational systems.

Example: a disk with $I = 2$ kg·m$^2$ spinning at 10 rad/s has $L = 20$ kg·m$^2$/s.

Conservation and Applications

When a skater pulls arms inward, moment of inertia drops and angular velocity rises so that $L$ stays nearly constant. Gyroscopes resist tipping because changing their angular momentum requires torque. Satellite attitude control relies on the same principle.

Related tools: Torque Calculator and Centripetal Force Calculator.

Frequently Asked Questions

What units does angular momentum use?

The SI unit is kg times meter squared per second. It can also be written as joule-seconds in rotational contexts.

How do I convert RPM to rad/s for this formula?

Multiply RPM by 2 pi and divide by 60. The calculator accepts RPM directly and converts internally.

Is angular momentum a vector?

Yes. It has both magnitude and direction along the rotation axis. This calculator computes the scalar magnitude for a single axis of rotation.

How does torque affect angular momentum?

Net external torque equals the rate of change of angular momentum. Constant torque produces steadily increasing or decreasing L over time.

What is moment of inertia?

It measures resistance to angular acceleration, depending on mass and how that mass is distributed relative to the rotation axis.

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Angular Momentum Calculator

What Is Angular Momentum?

Angular Momentum Formula

Conservation and Applications

Frequently Asked Questions

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