Final answer:
The angular velocity of the motorcycle wheel, which turns 10 π rad in 45.0 s, is π / 4.5 rad/s.
Step-by-step explanation:
The angular velocity of the motorcycle wheel is calculated using the formula ω = θ / t, where ω is the angular velocity, θ is the angle in radians through which the wheel turns, and t is the time taken for this rotation. Given that the motorcycle wheel turns 10 π rad during 45.0 s, we calculate the angular velocity as follows:
ω = θ / t = 10 π rad / 45.0 s = π / 4.5 rad/s
Thus, the angular velocity of the wheel is π / 4.5 rad/s.