Rotational mechanics tool

Angular Momentum Calculator

Solve angular momentum, moment of inertia, or angular velocity using L = Iω.

Enter two known values

Solve an angular momentum problem

Free tool
kg·m²/s

This is the value being calculated.

kg·m²

Resistance to changes in rotational motion.

rad/s

Rate of rotation in radians per second.

Use kilogram square meters per second for angular momentum, kilogram square meters for moment of inertia, and radians per second for angular velocity.

Try an example:

Your angular momentum result will appear here

Choose the missing variable and enter the other two known values.

Calculator guide

How this calculator works

Angular Momentum Calculator determines the rotational quantity of motion of an object based on moment of inertia and angular velocity. It helps physics students, engineers, and laboratory users analyze rotating systems such as flywheels, turbines, and aerospace mechanisms using rotational mechanics principles.

Formula explanation

Angular momentum describes rotational motion and depends on rotational inertia and angular velocity.

Formula

Angular Momentum = Moment of Inertia × Angular Velocity

Worked example

Example: Increasing rotational speed increases the angular momentum of a rotating object.

Assumptions

  • Moment of inertia and angular velocity values are measured accurately.
  • The rotating system follows classical rotational mechanics principles.
  • Input values use compatible units.

Examples

  • Example: Calculate angular momentum when moment of inertia and angular velocity are known.
  • Example: Engineers analyze flywheels, turbines, and rotating systems using angular momentum calculations.

Common mistakes

  • Confusing angular momentum with linear momentum.
  • Ignoring axis of rotation.
  • Using incorrect inertia values.

Variables

  • Moment of inertia
  • Angular velocity
  • Angular momentum
  • Mass distribution
  • Rotational axis
  • Measurement units

Limitations

  • Results depend on accurate inertia and angular velocity measurements.
  • Systems affected by external torque, friction, or changing mass distribution may require more advanced rotational analysis.

Scientific references

  • OpenStax University Physics: Rotational Motion
  • NIST SI Units and Measurement References
  • Classical mechanics principles

Content review

Reviewed by: ScienceCalcHub Physics Review Team | Last reviewed: 2026-08-30

Applications

  • Physics education
  • Rotational mechanics analysis
  • Engineering rotating system studies
  • Flywheel and turbine analysis
  • Laboratory angular motion experiments
  • Aerospace rotational systems

Frequently asked questions

How is angular momentum calculated?

Angular momentum is calculated by multiplying moment of inertia by angular velocity using the relationship L = Iω.

What factors affect angular momentum?

Angular momentum depends on mass distribution, rotational axis, moment of inertia, and angular velocity.

What is the SI unit of angular momentum?

The SI unit of angular momentum is kilogram meter squared per second (kg·m²/s).

What is the difference between angular and linear momentum?

Linear momentum describes motion in a straight line, while angular momentum describes rotational motion around an axis.

What is conservation of angular momentum?

Conservation of angular momentum states that the total angular momentum of an isolated system remains constant when no external torque acts on it.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the ScienceCalcHub Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Written by
ScienceCalcHub Editorial Team
Reviewed by
ScienceCalcHub Scientific Review Team
Review standard
Formula accuracy, units, examples, and educational clarity

Learn more about our formula-review and correction process, explore our calculation methodology, or view our scientific references.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently

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

  1. Write the formula: L = Iω.
  2. Substitute the values: L = 4 × 3.
  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

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

Calculator FAQ

How is angular momentum calculated?

Angular momentum is calculated by multiplying moment of inertia by angular velocity using the relationship L = Iω.

What factors affect angular momentum?

Angular momentum depends on mass distribution, rotational axis, moment of inertia, and angular velocity.

What is the SI unit of angular momentum?

The SI unit of angular momentum is kilogram meter squared per second (kg·m²/s).

What is the difference between angular and linear momentum?

Linear momentum describes motion in a straight line, while angular momentum describes rotational motion around an axis.

What is conservation of angular momentum?

Conservation of angular momentum states that the total angular momentum of an isolated system remains constant when no external torque acts on it.