A solid disk with mass 2 kg and radius 0.3 m has angular velocity ω = 20 rad/s. What is its rotational kinetic energy?

A solid disk with mass 2 kg and radius 0.3 m has angular velocity ω = 20 rad/s. What is its rotational kinetic energy?

• A. 18 J
• B. 9 J
• C. 36 J
• D. 72 J

Answer: (A)

Rotational kinetic energy comes from how much motion the object’s rotation stores: KE_rot = (1/2) I ω^2. For a solid disk, the moment of inertia is I = (1/2) m r^2. Plug in the numbers: I = (1/2) × 2 kg × (0.3 m)^2 = 0.5 × 2 × 0.09 = 0.09 kg·m^2. Then KE_rot = (1/2) × 0.09 × (20 rad/s)^2 = 0.045 × 400 = 18 J. So the rotational kinetic energy is 18 joules.

Rotational kinetic energy comes from how much motion the object’s rotation stores: KE_rot = (1/2) I ω^2. For a solid disk, the moment of inertia is I = (1/2) m r^2. Plug in the numbers: I = (1/2) × 2 kg × (0.3 m)^2 = 0.5 × 2 × 0.09 = 0.09 kg·m^2. Then KE_rot = (1/2) × 0.09 × (20 rad/s)^2 = 0.045 × 400 = 18 J. So the rotational kinetic energy is 18 joules.