Rotational Momentum Calculator

| Added in Physics

What is Angular Momentum?

Angular momentum (rotational momentum) measures the quantity of rotation an object has. It is the rotational equivalent of linear momentum and is conserved in isolated systems, making it a fundamental concept in physics.

This principle explains why a figure skater spins faster when they pull their arms in - they reduce their moment of inertia, so angular velocity must increase to conserve momentum.

The Formula

[L = I \times \omega]

Where:

  • L is angular momentum (kg-mยฒ/s)
  • I is moment of inertia (kg-mยฒ)
  • ฯ‰ (omega) is angular velocity (rad/s)

Calculation Example

For a disc with:

  • Moment of inertia: 30 kg-mยฒ
  • Angular velocity: 4 rad/s

[L = 30 \times 4 = 120 \text{ kg-mยฒ/s}]

The disc has an angular momentum of 120 kg-mยฒ/s.

Quick Reference

Variable Description Unit
L Angular momentum kg-mยฒ/s
I Moment of inertia kg-mยฒ
ฯ‰ Angular velocity rad/s

Applications

  • Figure skating: Spin speed changes with arm position
  • Astronomy: Explains rotation of planets and galaxies
  • Engineering: Flywheel and gyroscope design
  • Sports: Diving, gymnastics, and throwing motions

Frequently Asked Questions

Angular momentum (also called rotational momentum) is a measure of how much rotational motion an object has. It depends on both how fast the object spins and how its mass is distributed.

Angular momentum is conserved when no external torque acts on a system. This is why a figure skater spins faster when pulling their arms in - reducing moment of inertia increases angular velocity.

Moment of inertia measures how difficult it is to change an objects rotational speed. It depends on mass and how that mass is distributed relative to the rotation axis.

Angular momentum is measured in kg-mยฒ/s in SI units, representing the product of moment of inertia (kg-mยฒ) and angular velocity (rad/s).