Final answer:
The average angular acceleration of the fan blade is found by dividing the change in angular velocity by the time taken. In this case, it is 0.5 rad/s².
Step-by-step explanation:
The student has asked how to find the average angular acceleration of a fan blade that starts from rest and reaches an angular velocity of 5 radians per second after 10 seconds. To solve this, we use the definition of average angular acceleration, which is the change in angular velocity divided by the time taken to make that change. Here, the initial angular velocity (ω0) is 0 rad/s (as it starts from rest), the final angular velocity (ω) is 5 rad/s, and the time (δt) is 10 seconds. The average angular acceleration (α) can be calculated using the formula α = (ω - ω0) / δt.
Plugging in the values we have: α = (5 rad/s - 0 rad/s) / 10 s = 0.5 rad/s².
Therefore, the average angular acceleration of the fan blade is 0.5 rad/s².