Angular Momentum
Simple Explanation
Angular momentum measures how much rotational motion an object has — it depends on the object's moment of inertia and its angular velocity, playing the same role for rotation that ordinary (linear) momentum plays for straight-line motion.
Why Do We Need It?
Angular momentum is central to understanding why spinning objects behave the way they do, and sets up the law of conservation of angular momentum, one of the most powerful principles in rotational physics.
Formula
Angular Momentum
L = Iω
Angular momentum measures the "quantity of rotational motion" an object has — the rotational equivalent of linear momentum (p = mv).
- L
- — Angular momentum, in kg·m²/s
- I
- — Moment of inertia, in kg·m²
- ω
- — Angular velocity, in rad/s
When to use it: Use to calculate the angular momentum of a rotating object, and as the basis for applying conservation of angular momentum.
Worked Example
Calculating angular momentum
A wheel with moment of inertia 4 kg·m² spins at an angular velocity of 5 rad/s. Find its angular momentum.
Why Does This Work?
Angular momentum combines how the mass is distributed (moment of inertia, I) with how fast it is rotating (angular velocity, ω) into one quantity — this mirrors how linear momentum (p = mv) combines mass and linear velocity, since both describe the "quantity of motion" in their respective systems.
Real-Life Example
A spinning gyroscope resisting tipping over
A fast-spinning gyroscope resists being tipped over, staying remarkably stable.
A rapidly spinning gyroscope has a large angular momentum — since angular momentum resists changes in the same way linear momentum does, a large angular momentum makes the gyroscope's spin axis strongly resist being reoriented.
Practice
A disc with moment of inertia 2.5 kg·m² rotates at 8 rad/s. Find its angular momentum.
MediumCommon mistake
Confusing angular momentum (L = Iω, for rotating objects) with linear momentum (p = mv, for objects moving in a straight line) — they describe fundamentally different kinds of motion and use different quantities.
Quick Review
- L = Iω is the rotational equivalent of linear momentum p = mv.
- Depends on both moment of inertia and angular velocity.
- A large angular momentum makes an object strongly resist changes to its spin.