Two uniform solid cylinders, each rotating about its central (longitudinal) axis, have the same mass of 3.44 kg and rotate with the same angular speed of 430 rad/s, but they differ in radius. What is the rotational kinetic energy of (a) the smaller cylinder, of radius 0.356 m, and (b) the larger cylinder, of radius 0.775 m?

(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.

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