An electric fan is turned off, and its angular velocity decreases uniformly from

ID: 1778154 • Letter: A

Question

An electric fan is turned off, and its angular velocity decreases uniformly from 670 rev/min to 150 rev/min in 2.50 s .

Part A

Find the angular acceleration in rev/s2.

Part B

Find the number of revolutions made by the motor in the 2.50 s interval.

Part 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?

An electric fan is turned off, and its angular velocity decreases uniformly from 670 rev/min to 150 rev/min in 2.50 s .

Part A

Find the angular acceleration in rev/s2.

Part B

Find the number of revolutions made by the motor in the 2.50 s interval.

Part 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?

Here ,

initial angular speed , wi = 670 rev/min

wi = 70.15 rad/s

final angular speed , wf = 150 rev/min = 150 * 2pi/60 rad/s

wf = 15.71 rad/s

t = 2.50 s

part A) angular acceleration = change in angular speed/t

angular acceleration = (-70.15 + 15.71)/2.50

angular acceleration = -21.8 rad/s^2

angular acceleration = -3.47 rev/s^2

part B)

number of revs made = u * t + 0.50 * a * t^2

number of revs made = 70.15/2pi * 2.50 - 0.50 * 3.47 * 2.50^2

number of revs made = 17.1 revs

part C)

time taken to stop = (0 - 15.71)/(-21.8)

time taken to stop = 0.72 s

further time taken is 0.72 s

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