# 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

$L=r\times&space;p$

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

$=\frac{mr^{2}}{2}$

I= 200*0.5*0.5/2

I= 25 kg m2

The angular momentum is given by L = $I\omega$

L = 25 x 100

= 2500 kg m2/s

Problem 2: Compute the angular momentum of the rod of radius 1 m and mass 2 kg spinning with velocity 5 rad/s?
=  $\inline \frac{mr^{2}}{2 }\omega$
$= \frac{2*1^{2}}{2 }5$