What is angular momentum?

Angular momentum (L) is the rotational analog of linear momentum. It is defined as L = I x omega, where I is the moment of inertia (kg·m²) and omega is the angular velocity (rad/s). The SI unit of angular momentum is kg·m²/s.

What is moment of inertia?

Moment of inertia (I) quantifies how difficult it is to change an object's rotational motion. It depends on the mass distribution relative to the rotation axis. A solid cylinder has I = 1/2 m r², while a hollow cylinder (thin ring) has I = m r².

How do I convert RPM to rad/s?

Multiply RPM by 2π/60 (approximately 0.10472). For example, 100 RPM = 100 × 2π/60 ≈ 10.472 rad/s. This calculator performs the conversion automatically when you select RPM as the unit.

Why does a thin rod use half-length as input?

The formula for a thin rod rotating about its center is I = 1/12 m L², where L is the full length. This calculator accepts half-length (L/2) as the radius input to keep the interface consistent. Internally it computes the full length as 2 × input.

Is angular momentum conserved?

Yes. In the absence of external torques, the total angular momentum of a system is conserved. This is the principle behind a figure skater spinning faster by pulling in their arms — reducing I causes omega to increase so that L stays constant.

What units does this calculator use?

Inputs are in kilograms (kg) for mass and meters (m) for radius. Angular velocity is accepted in rad/s or RPM. Outputs are in kg·m² for moment of inertia and kg·m²/s for angular momentum.

Angular Momentum Calculator

Name: Angular Momentum Calculator
Availability: InStock
Author: Nham Vu

Compute angular momentum L = I x omega for solid cylinders, hollow cylinders, solid spheres, and thin rods. Supports RPM and rad/s input.

Input Parameters

Object Shape

I = 1/2 × m × r²

Mass (m)

Radius (r)

Angular Velocity (ω)

Results

Enter values and click Calculate

Sample Test Cases

Shape	m (kg)	r (m)	ω (rad/s)	I (kg·m²)	L (kg·m²/s)
Solid Cylinder	2	0.5	10	0.25	2.5
Solid Sphere	5	0.3	20	0.18	3.6
Hollow Cylinder	3	0.4	15	0.48	7.2
Thin Rod (half-len = 0.5 m)	4	0.5	8	0.3333	2.667

Click any row to load that case into the calculator.

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Summary

Compute angular momentum L = I x omega for solid cylinders, hollow cylinders, solid spheres, and thin rods. Supports RPM and rad/s input.

How it works

Select the object shape from the dropdown — the moment of inertia formula updates automatically.
Enter the mass in kilograms.
Enter the radius (or half-length for a thin rod) in meters.
Enter the angular velocity in rad/s or RPM — the calculator converts RPM to rad/s automatically.
Click Calculate to see the moment of inertia (I) and angular momentum (L).
Use the sample test cases below the calculator to verify correctness.

Use cases

Calculating the angular momentum of a spinning flywheel or disk.
Analyzing rotational motion in physics homework and exams.
Verifying moment of inertia values for common rigid-body shapes.
Converting between RPM and rad/s for angular velocity inputs.
Estimating angular momentum of planetary bodies or rotating machinery.
Teaching rotational kinematics and inertia concepts.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu