A uniform solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 33.4 rpm. What is its kinetic energy?

0.092 J

Explanation:

Rotational kinetic energy is:

RE = ½ Iω²

where I is the moment of inertia and ω is the angular speed.

For a solid cylinder, I = ½ mr².

RE = ½ (½ mr²) ω²

RE = ¼ mr²ω²

Convert ω from rpm to rad/s.

33.4 rev/min * (2π rad/rev) * (1 min / 60 s) = 3.50 rad/s

Plug in values and solve:

RE = ¼ (3.0 kg) (0.10 m) ² (3.50 rad/s) ²

RE = 0.092 J