Question

An electric fan is turned off, and its angular velocity decreases uniformly from 550 rev/min to 150 rev/min in a time interval of length 3.85

A)Find the angular acceleration in rev/s2.

B)Find the number of revolutions made by the motor in the time interval of length 3.85 s

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?

Answer 1

initial velocity = 550 rev / min or 550 * 2 * pi / 60 rad/sec

final velocity = 150 rev/min or 150 * 2 * pi / 60 rad/sec

acceleration = change in velocity / time

acceleration = (550 * 2 * pi / 60 - 150 * 2 * pi / 60) / 3.85

angular acceleration = 10.8799746 rad/sec^2

by third equation od motion

v^2 = u^2 - 2as

(150 * 2 * pi / 60)^2 = (550 * 2 * pi / 60)^2 - 2 * 10.8799746 * s

s = 141.109 rad or 22.46 rev

number of revolution made = 22.46 rev

v = u + at

0 = (550 * 2 * pi / 60) - 10.8799746 * t

t = 5.293 sec

more time requied = 5.293 - 3.85

more time required = 1.443 sec