Table of Contents
What Is Angular Momentum?
Angular momentum is the rotational equivalent of linear momentum. It measures the quantity of rotation an object has, considering both how fast it spins and how its mass is distributed. For a rigid body rotating about a fixed axis, angular momentum equals the moment of inertia times the angular velocity.
Angular momentum is one of the most important conserved quantities in physics. The conservation of angular momentum explains why ice skaters spin faster when they pull in their arms, why gyroscopes maintain their orientation, why planets speed up near perihelion, and why neutron stars spin incredibly fast.
Angular Momentum Formula
Where L is angular momentum in kg m²/s, I is moment of inertia in kg m², and omega is angular velocity in rad/s.
Moment of Inertia Formulas
| Shape | Formula |
|---|---|
| Solid Sphere | I = (2/5)mr² |
| Hollow Sphere | I = (2/3)mr² |
| Solid Cylinder/Disk | I = (1/2)mr² |
| Thin Ring | I = mr² |
| Thin Rod (center) | I = (1/12)mL² |
| Point Mass | I = mr² |
FAQ
Why do ice skaters spin faster pulling arms in?
Angular momentum L = I*omega is conserved. When the skater pulls arms in, the moment of inertia I decreases. To keep L constant, omega (spin rate) must increase proportionally. This is a dramatic demonstration of conservation of angular momentum.
Is angular momentum always conserved?
Angular momentum is conserved when no external torque acts on the system. In practice, friction and air resistance provide small external torques that gradually change angular momentum. In isolated systems like orbiting planets, angular momentum is very precisely conserved.
What are the units of angular momentum?
Angular momentum is measured in kg m²/s (kilogram meters squared per second) in SI units. In quantum mechanics, angular momentum comes in discrete multiples of the reduced Planck constant hbar = 1.055 × 10^-34 kg m²/s, which sets the fundamental scale of atomic angular momentum.