Angular Momentum Formula

What is Angular Momentum?

Angular momentum can be thought of as how much something is rotating. For instance, take a figure skater who is spinning around. When they spin faster or when they extend their arms out, their angular momentum varies.

Definition of Angular Momentum

Angular momentum is a property that describes the tendency of an object to keep rotating. This is a vector quantity that describes the type of rotational motion the object performs around a certain point or axis. It depends directly on the magnitude of its rotational speed, but also on how the mass of the object is distributed about the point or axis of rotation. The resulting quantity 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=rp

where,

r = length vector

p = linear momentum

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

Example:

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

Solution:

Given : Mass M = 200 kg,

Angular speed ω = 100 ms-1,

Radius r = 0.5 m,

Since it is a solid cylinder, 

Moment of Inertia I=mr22

I = 200 x 0.5 x 0.5/2

I = 25 kg m2

Angular momentum is given by

L=I

L = 25 x 100

= 2500 kg m2 / s