angular momentum formulas and interpretation
Angular momentum describes rotational motion about a specified axis.
For a rigid body it depends on moment of inertia and angular velocity; for a perpendicular point-particle path it depends on mass, speed, and radius.
How to use the angular momentum calculator
- Choose a model: Select the physical relationship that matches the known values.
- Choose the unknown: Select the quantity you need to calculate.
- Enter values and units: Provide every requested measurement using consistent units.
- Calculate: Check the formula, converted result, sign, and units.
Formula and variables
Rigid-body angular momentum equals moment of inertia multiplied by angular velocity.
L = Iω- L — Angular momentum
- Rotational momentum (kg·m²/s)
- I — Moment of inertia
- Rotational inertia about the axis (kg·m²)
- ω — Angular velocity
- Rotation rate (rad/s)
Flywheel example
A flywheel has inertia 4 kg·m² and rotates at 10 rad/s.
- Moment of inertia
- 4 kg·m²
- Angular velocity
- 10 rad/s
- L = 4 × 10
- L = 40 kg·m²/s
Result: Angular momentum is 40 kg·m²/s.
The flywheel carries 40 kg·m²/s of angular momentum about its axis.
Understanding your results
Interpreting the result
Angular momentum increases in direct proportion to inertia or angular velocity.
A sign indicates direction only when a consistent rotational sign convention is used.
Assumptions
- Rotation is evaluated about a specified axis.
- Inputs are converted through coherent SI units.
- The selected formula adequately represents the physical system.
Limitations
- The calculator does not simulate time-varying inputs.
- Vector directions and multiple axes must be resolved separately.
- Losses such as friction are not added unless represented in the entered net value.
Common mistakes
- Mixing RPM with radians per second.
- Using diameter instead of radius.
- Entering a zero divisor.
- Ignoring the direction represented by a negative value.
Practical use cases
Physics and education
Check rotational kinematics and dynamics exercises.
Machines and mechanisms
Estimate quantities for wheels, shafts, rotors, and rotating equipment.
Frequently asked questions
Why are radians used in rotational formulas?
Radians make angular and linear relationships dimensionally coherent without an extra conversion factor.
Can the result be negative?
Yes. A negative value means the quantity points opposite the direction chosen as positive.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.