Question

A body is rotating with kinetic energy E. If angular velocity of body is increased to three times of initial angular velocity then kinetic energy become nE. Find n.

Answer 1

The kinetic energy of a rotating body can be expressed as:
E = \((\frac{1}{2}) I w^2\)
where,
E is the initial kinetic energy,
I is the moment of inertia,
w is the initial angular velocity.
If the angular velocity is increased by a factor of three, the new angular velocity is 3w.
The kinetic energy of the body can be expressed as:
nE = \((\frac{1}{2}) I 3w^2\) = \(9(\frac{1}{2}) I w^2\) = 9E
Therefore, n = 9. 
So, the kinetic energy becomes nine times the initial kinetic energy when the angular velocity is increased to three times the initial angular velocity.
Answer. 9