Two uniform solid cylinders, each rotating about its central (longitudinal) axis, have the same mass of 2.88 kg and rotate with the same angular speed of 257 rad/s, but they differ in radius. What is the rotational kinetic energy of (a) the smaller cylinder, of radius 0.319 m, and (b) the larger cylinder, of radius 0.605 m

(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

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