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A certain pulley is a uniform disk of mass 2.7 kg and radius 0.25 m. A...

A certain pulley is a uniform disk of mass 2.7 kg and radius 0.25 m. A rope applies a constant torque to the pulley, which is free to rotate without friction, resulting in an angular acceleration of 0.12 rad/s2. The pulley starts at rest at time t = 0 s. What is its rotational kinetic energy at t = 2.2 s?

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Answer #1

w = at
E = Iw^2 / 2
I = mr^2 / 2

The moment of inertia is:
2.7 * 0.25^2 / 2 kg m^2

The angular velocity at time 2.2 sec. is:
0.12 * 2.2 rad / sec.

The rotational KE is:
(2.7 * 0.25^2 / 2) (0.12 * 2.2)^2 / 2
= 2.94 * 10^(-3) J.

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