Final answer:
The rotational kinetic energy of a bicycle wheel with 24-inch diameter wheels traveling at 12 mi/h is 2666.69 Joules.
Step-by-step explanation:
The rotational kinetic energy of a bicycle wheel can be calculated using the formula:
KE = 1/2 * I * ω²
Where KE is the rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity.
Given the diameter of the wheel is 24 inches, the radius would be 12 inches or 0.3048 meters. Substituting the values into the formula and converting the angular velocity from rad/s to s²:
KE = 1/2 * (m * R²) * (ω²)
KE = 1/2 * (12.0 kg * (0.3048 m)²) * (120 rad/s)²
KE = 2666.69 Joules