Question

A solid cylinder is rotating at 20 rad/2s. If the moment of inertia of the cylinder is increased by a factor of 3.4, what is the new rotational speed? What is the ratio of the new rotational kinetic energy to the original rotational kinetic energy?

Answer 1

here,

initial angular speed , w0 = 20 rad/2s = 10 rad/s

the new rotational inertia , I = 3.4 * I0

let the new rotational speed be w

using conservation of angular momentum

I0 * w0 = I * w

I0 * 10 = 3.4 * I0 * w

solving for w

w = 2.94 rad/s

the new rotational speed is 2.94 rad/s

the ratio of the new rotational kinetic energy to the original rotational kinetic energy , R = 0.5 * I * w^2 /( 0.5 * I0 * w0^2)

R = 0.5 * 3.4 * I0 * 2.94^2 / ( 0.5 * I0 * 10^2)

R = 0.29