Physics overview
What is angular momentum?
Angular momentum describes the rotational motion of an object. It depends on the object's moment of inertia and angular velocity.
Formula
Angular momentum formula
Angular MomentumL = Iω
- L is angular momentum in kg·m²/s.
- I is moment of inertia in kg·m².
- ω is angular velocity in rad/s.
Worked example
An object has I = 4 kg·m² and ω = 3 rad/s
- Write the formula: L = Iω.
- Substitute the values: L = 4 × 3.
- Calculate angular momentum: L = 12 kg·m²/s.
Rearranged equations
Solve for moment of inertia or angular velocity
Moment of inertia
I = L ÷ ω
Divide angular momentum by angular velocity.
Angular velocity
ω = L ÷ I
Divide angular momentum by moment of inertia.
Conservation principle
Conservation of angular momentum
When no external torque acts on a system, its total angular momentum remains constant. A decrease in moment of inertia therefore causes angular velocity to increase.
Physical relationship
Moment of inertia and speed both affect L
Angular momentum increases when moment of inertia increases, angular velocity increases, or both increase.
Units
Standard SI units
Use kilogram square meters per second for angular momentum, kilogram square meters for moment of inertia, and radians per second for angular velocity.
Real-world applications
Where angular momentum is used
- Rotating wheels and flywheels.
- Spinning athletes and ice skaters.
- Planetary and satellite motion.
- Gyroscopes and navigation systems.
- Rotating machinery and turbines.
Calculation limits
Important assumptions
- All entered values must be greater than zero.
- Moment of inertia is defined for the selected rotation axis.
- Angular velocity is expressed in radians per second.
- Vector direction is not represented.
- Units are not converted automatically.
Related tools
Continue your rotational analysis
Use the Moment of Inertia Calculator to calculate rotational inertia for common shapes.
Use the Angular Velocity Calculator to calculate angular velocity, angular displacement, or time.
Questions and answers
Angular momentum calculator FAQ
What formula does the angular momentum calculator use?
It uses L = Iω, where angular momentum equals moment of inertia multiplied by angular velocity.
What is angular momentum?
Angular momentum is the rotational equivalent of linear momentum and describes the rotational motion of an object.
How do you calculate moment of inertia from angular momentum?
Divide angular momentum by angular velocity using I = L ÷ ω.
What units are used for angular momentum?
Angular momentum is measured in kilogram square meters per second, written as kg·m²/s.