 # Angular Momentum Formula

## Definition

The degree to which a body rotates gives its angular momentum. It is defined as the product of the moment of inertia “I” and the angular velocity “ω”

L =Iω

Angular momentum in terms of Linear momentum can be written as

$$\begin{array}{l}L=r\times p\end{array}$$

where,

r = length vector

p = linear momentum

The unit for Angular momentum is given as kilogram meter square per second (kg m2/s). Angular Momentum formula is made use of in computing the angular momentum of the particle and also to find the parameters associated to it.

## Angular Momentum Numericals

Problem 1: A solid cylinder of mass 200 kg rotates about its axis with an angular speed of 100ms-1. If the radius of the cylinder is 0.5 m. Compute the angular momentum of the cylinder about its axis?

Given: Mass M = 200 kg,
Angular speed ω = 100 ms-1,

Since it is a solid cylinder, Moment of Inertia I

$$\begin{array}{l}=\frac{mr^2}{2}\end{array}$$

I= 200*0.5*0.5/2

I= 25 kg m2

The angular momentum is given by

$$\begin{array}{l}L = I\omega \end{array}$$

L = 25 x 100

= 2500 kg m2/s