Angular Momentum Calculator

Created by Luciano Mino
Last updated: Sep 20, 2022

Our angular momentum calculator is the perfect tool for obtaining the angular momentum of a point object rotating around a fixed origin or finding the angular momentum of a rotating rigid body.

Keep reading while we walk you through everything you need to know about angular momentum, including:

  • What angular momentum is;
  • How to find the angular momentum of a particle or rigid body;
  • What is the unit for angular momentum; and
  • More!

What is angular momentum?

The angular momentum is the linear momentum analog for rotations. It's a vector quantity describing the rotational momentum of an object.

Like linear momentum, it's a conserved quantity: given no external torques, it remains constant.

💡 Read more about this in our conservation of momentum calculator.

We can define two types of angular momentum:

  • The angular momentum of a point particle relative to a fixed point in space; and
  • The angular momentum of a rigid body around its center of rotation.

Let's now look at how to calculate angular momentum.

Angular momentum formula

As we said, we'll have two analogous formulas for angular momentum: for point particles and rigid bodies.

Angular momentum of a point particle

For a point particle rotating around a fixed point (a satellite orbiting the Earth, for example), the angular momentum L\vec{L} is the cross product between the position vector r\vec{r} and the linear momentum of the particle p\vec{p}:

L=r×p\vec{L} = \vec{r} \times \vec{p}

and in terms of the particle's velocity v\vec{v}:

L=mr×v\vec{L} = m \vec{r} \times \vec{v}
Right-hand rule example
Right-hand rule example

Its orientation is given by the right-hand rule: we wrap our right-hand fingers around the trajectory of the particle, and our thumb will point in the same direction as the resulting angular momentum.

Angular momentum of a rotating rigid body

For a rotating rigid body, such as the Earth, the angular momentum about an axis is the product between its moment of inertia II and its angular velocity ω\vec{\omega}:

L=Iω\vec{L} = I \vec{\omega}

🙋 You can find the angular momentum for either case with our angular momentum calculator. Simply select the formula at the top of the calculator and start experimenting with it!

What is the unit for angular momentum

The SI, International System of Units unit for angular momentum is the kilogram meter squared per second (kg ⋅ m²/s).

With our angular momentum calculator, you can input the parameters using any unit, and it will automatically convert the angular momentum to this SI unit.

Luciano Mino
Formula
Object moving around a central point
Mass (m)
kg
Radius (r)
m
Velocity (v)
m/s
Angular momentum (L)
kg ⋅ m² /s
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