Answer:
(a) 
(b) 
Explanation:
Given data
The angular velocity of two cylinders ω=257 rad/s
The mass of the two cylinders m=2.88 kg
The radius of small cylinder r₁=0.319 m
The radius of larger cylinder r₂=0.605 m
For Part (a)
The rotational kinetic energy of the cylinder is given by:

Where I is rotational of inertia of solid cylinder about its central axis.
So

Substitute the given values
So

For Part (b)

Substitute the given values
