Angular Momentum Calculator: Rotational Motion

What is Angular Momentum?

Angular momentum (L) is the rotational equivalent of linear momentum. It measures how much rotational motion an object has and is conserved in the absence of external torques. This conservation principle explains why a spinning ice skater speeds up when pulling in their arms.

🌀 Angular Momentum Calculator

Use our free calculator for instant, accurate results.

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📐 Formula

L = I × ω

L = angular momentum (kg·m²/s), I = moment of inertia (kg·m²), ω = angular velocity (rad/s). For a point mass: L = m × v × r.

📝 Worked Example

A spinning disk: I = 0.5 kg·m², ω = 4 rad/s:
L = 0.5 × 4 = 2 kg·m²/s
If I decreases to 0.25 (arms pulled in): ω = 2/0.25 = 8 rad/s (conservation law)

📝 How to Use the Calculator

Select Object TypeChoose point mass, disk, sphere, or ring to get the right moment of inertia.

Enter Mass & DimensionsInput mass (kg) and relevant radius or length.

Enter Angular VelocityProvide ω in rad/s or RPM.

Get Angular MomentumView L in kg·m²/s and see conservation scenarios.

❓ FAQ

Is angular momentum always conserved?

It is conserved when net external torque = 0. Friction and air resistance introduce external torques that violate conservation.

What is the difference between angular momentum and torque?

Torque (τ) is the cause of change in angular momentum: τ = dL/dt. No torque means constant angular momentum.

What is Angular Momentum?