Angular Momentum Units

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In the linear motion, momentum is the product of mass and velocity. In the same way, in circular motion angular momentum is a product of the moment of inertia and the angular velocity of the object. Angular velocity is a vector quantity that means it has magnitude and direction.

Angular momentum is denoted by “L”.

                             L = Iω

Where, I = moment of inertia of an object

          ω = angular velocity

The dimensional formula for moment of inertia = kg m^2 = M^1 L^2 T^0

And Dimensional formula for angular velocity = rad/sec = M^0 L^0 T^-1

Thus, Dimensional formula for angular momentum = M^1 L^2 T^-1

Therefore, Unit of angular momentum = Kg m^2/sec.

Example: Calculate the angular momentum of the rod of radius 4 m and mass 6 kg rotating with velocity 7 rad/s?

Solution: Given that,

          Angular velocity, ω = 7 rad/s

                   Radius, r = 4 m

                   Mass, m = 6 kg

So that, Angular momentum, L = I ω

                                                = mr^2 ω

                                                = 6(4)^2 (7)

                                                = 672 Kgm^2s^-1.

 Example: What is the angular momentum of a thin hoop of radius 2 m and mass 1 kg that is rotating at a angular velocity of 4 rad/s?

Solution: Given that,

          Angular velocity, ω = 4 rad/sec

                   Radius, r = 2 m

                   Mass, m = 1 Kg

So that, Angular momentum, L = Iω

                                                 = mr^2 ω

                                                = 1(2)^2 (4)

                                                = 16 Kgm^2 s^-1

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