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

Angular momentum formula

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?
Answer:

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

Angular momentum formula 2

I= 200*0.5*0.5/2

I= 25 kg m2

The angular momentum is given by L = Angular momentum Fomula 3

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?
Answer:

Given: Radius r = 1 m,
Mass M = 2 kg,
Angular Velocity ω = 5 rad/s
The angular momentum is given as L = I ω

=  Angular momentum Fomula 4

Angular momentum Fomula 5

L = 5 kg m2 s-1.

 

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