Question

A particle performs uniform circular motion with an angular momentum l. If the frequency

Answer 1

We have,

Angular momentum = L = Iω

Where, I is the moment of inertia and ω is the angular velocity.

So frequency of revolution is, f = ω/2π

=> ω = 2πf

Kinetic energy, K = ½ Iω2 = ½ Lω =  ½ (2πfL) = πfL …………..(1)

Now, frequency is doubled, so, let f/ = 2f = 2(ω/2π) = ω/π

The kinetic energy is halved, so, K/ = K/2 = ½ (πfL)

If L/ is the new angular momentum, then using (1) we can write,

K/ = πf/L/

=> ½ (πfL) = π(2f)L/

=> L/ = L/4

So, angular momentum becomes one fourth of its original value.