Final answer:
The average angular acceleration of the fan during this time is approximately 73.3 rad/s².
Step-by-step explanation:
To find the average angular acceleration of the fan, we need to use the formula:
Angular acceleration (α) = (final angular velocity - initial angular velocity) / time
Given that the fan goes from rest (0 rpm) to 2100 rpm in 5.0 s, the initial angular velocity is 0 rpm and the final angular velocity is 2100 rpm. Converting the angular velocities to rad/s, we have 0 rad/s and 220 π rad/min respectively. This gives us:
Angular acceleration (α) = (220 π rad/min - 0 rad/s) / 5.0 s
Converting minutes to seconds, we find:
Angular acceleration (α) = 220 π rad/min = (220 π rad/min)/(60 s/min) = 220 π / 60 rad/s
So the average angular acceleration of the fan during this time is approximately:
α = 220 π / 60 rad/s = 73.3 rad/s²