Angular Momentum Calculator

Angular Momentum Calculator

Calculate rotational momentum, a key conserved quantity in physics.

Calculate Angular Momentum

Angular Momentum
50.00 kg·m²/s

What is Angular Momentum?

Angular momentum (L) is the rotational equivalent of linear momentum. It measures the quantity of rotation of a body about an axis and is one of the most fundamental conserved quantities in physics.

Angular momentum is conserved in isolated systems. This principle explains why ice skaters spin faster when pulling in their arms, why cats land on their feet, and why gyroscopes remain stable. The formula is simply: L = I·ω.

Angular momentum is a vector quantity with both magnitude and direction. In quantum mechanics, angular momentum is quantized, appearing in atomic models and electron behavior.

How to Calculate

L = I × ω

Where: L = angular momentum (kg·m²/s), I = moment of inertia (kg·m²), ω = angular velocity (rad/s)

Example: Figure Skater Spinning

Skater with arms extended: I = 6 kg·m² rotating at 2 rad/s

L = 6 × 2 = 12 kg·m²/s

When arms pull in, I decreases, so ω increases to conserve L.

FAQ

What does conservation of angular momentum mean?

In an isolated system with no external torque, total angular momentum remains constant, even if the object's shape or rotation changes.

Why do figure skaters spin faster when pulling arms in?

Pulling in arms reduces moment of inertia (I). Since L is conserved, angular velocity (ω) must increase: L = I × ω.

Is angular momentum used in quantum mechanics?

Yes, heavily. Angular momentum is quantized in atoms, determining electron orbitals and chemical properties.

What real applications exist?

Gyroscopes, spacecraft attitude control, turbines, motors, and any rotating systems where stability matters.

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