Final answer:
The angular acceleration is -1.43 rev/s². The number of revolutions made by the fan blades is -1870.5 rev. It will take an additional 125.87 seconds for the fan to come to rest.
Step-by-step explanation:
To find the angular acceleration, we can use the formula:
Angular acceleration = (final angular velocity - initial angular velocity) / time
Substituting the given values:
Angular acceleration = (180 rev/min - 550 rev/min) / 4.30 s = -1.43 rev/s²
For part B, the number of revolutions made by the fan blades can be found using the formula:
Number of revolutions = (final angular velocity - initial angular velocity) * time
Substituting the given values:
Number of revolutions = (180 rev/min - 550 rev/min) * 4.30 s = -1870.5 rev
For part C, the time required for the fan to come to rest can be found using the formula:
Time = (final angular velocity - initial angular velocity) / angular acceleration
Substituting the given values:
Time = (0 rev/min - 180 rev/min) / -1.43 rev/s² = 125.87 s