Angular Momentum
Calculate angular momentum for rotating objects.
Covers both point particles and rigid bodies.
The Formulas
Point particle: L = m × v × r × sin(θ)
Rotating body: L = I × ω
Rotating body: L = I × ω
Angular momentum measures how much rotational motion an object has. Like linear momentum, angular momentum is conserved when no external torques act on a system.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| L | Angular momentum | kg·m²/s |
| m | Mass of the particle | kg |
| v | Velocity | m/s |
| r | Distance from the axis of rotation | m |
| θ | Angle between r and v vectors | degrees or radians |
| I | Moment of inertia | kg·m² |
| ω | Angular velocity | rad/s |
Example 1
A 2 kg ball moves at 5 m/s in a circle of radius 3 m
L = m × v × r (θ = 90°, sin(90°) = 1)
L = 2 × 5 × 3
= 30 kg·m²/s
Example 2
A solid disk (I = 0.5 kg·m²) spins at 10 rad/s
L = I × ω = 0.5 × 10
= 5 kg·m²/s
When to Use It
Use angular momentum when:
- Analyzing spinning objects (wheels, planets, figure skaters)
- Applying conservation of angular momentum (e.g., a skater pulling arms in spins faster)
- Studying orbital mechanics and satellite motion
- Solving rotational dynamics problems in physics