Answer:
(a) 20,154.1 J
(b) 95,223.5 J
Explanation:
The expression for the moment of inertia for the uniform solid cylinder is as follows;

Here, I is the moment of inertia, r is the radius and m is the mass of the object.
The expression for the rotational kinetic energy is as follows;

Here, K is the rotational kinetic energy and
is the angular velocity.
(a)
Calculate the moment of inertia of the smaller solid cylinder.

Put m= 3.44 kg and r= 0.356 m.


Calculate the rotational kinetic energy of the smaller cylinder.

Put
and
.

K= 20,154.1 J
Therefore, the rotational kinetic energy for the smaller cylinder is 20,154.1 J.
(b)
Calculate the moment of inertia of the larger solid cylinder.

Put m= 3.44 kg and r= 0.775 m.


Calculate the rotational kinetic energy of the smaller cylinder.

Put
and
.

K= 95,223.5 J
Therefore, the rotational kinetic energy for the larger cylinder is 95,223.5 J.