Question

An electric fan is turned off, and its angular velocity decreases uniformly from 550 rev/min to 180 rev/min in a time interval of length 4.30 s.

A.) Find the angular acceleration in revolutions per second per second.
= -1.43 rev/s^2
B.) Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A.
= _________? rev
C.) How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A?
= ____________? s

Answer 1

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