Angular Momentum Formula

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Angular momentum is the momentum of an object moving in circular motion. We can define it as the product of the moment of inertia and angular velocity.  Angular momentum is represented by “L”.

L = I ω

Where, I = moment of inertia

  ω = angular velocity

Unit of angular momentum is kg m^2/sec.

Relation between Linear and angular momentum is:

   L = r x p

Where, r = radius of the circular path.

 p = linear momentum.

Example: A solid cylinder of mass 450 kg rotates about its axis with angular speed of 60 radian s^-1. If the radius of the cylinder is 0.25 m. Calculate the angular momentum of the cylinder about its axis?

Solution: We have given that,

          Angular velocity, ω = 60 radian/sec

          Radius, r = 0.25 m

          Mass, m = 450 kg

So that, Moment of inertia, I = ½ mr^2

                                            = ½ (450)(0.25)^2 = 14.06 kg m^2

Now we have a formula for angular momentum,

                   L = I ω

                      = 14.06 (60) = 843.75 Kgm^2 s^-1.

Example: What is the angular momentum of a thin hoop of radius 3 m and mass 4 kg that is rotating at a angular velocity of 6 rad/s?

Solution: Given that,

          Angular velocity, ω = 6 rad/sec

                   Radius, r = 3 m

                   Mass, m = 4 Kg

So that, Angular momentum, L = Iω

                                                 = mr^2 ω

                                                 = 4(3)^2 (6)

                                                = 216 Kgm^2 s^-1.


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