Question

An electric fan is turned off, and its angular velocity decreases uniformly from 570 rev/min to 250 rev/min in 3.00 s .

Find the angular acceleration in rev/s2.

Find the number of revolutions made by the motor in the 3.00 s interval.

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?

Answer 1

initial angular speed wi = 570 rev/min

wi = 570 x 2pi rad / 60 sec = 59.69 rad/s

final angular speed wf = 250 rev/min

wf = 250 x 2pi rad / 60 sec = 26.18 rad/s

using wf = wi + alpha*t

26.18 = 59.69 + alpha*3

alpha = - 11.17 rad/s^2 = - 11.17 x (1/2pi rev ) / sec   = - 1.78 rev/s^2

using wf^2 - wi^2 = 2 x alpha x theta

26.18^2 - 59.69^2 = 2 x -11.17 x theta

theta = 128.81 rad   = 128.81/2pi = 20.50 rev.

using wf = wi + alpha*t

0 = 59.69   - 11.17t

t = 5.34 sec