Question

An electric fan is turned off, and its angular velocity decreases uniformly from 540 rev/min to 220 rev/min in a time interval of length 3.85 s . (a) Find the angular acceleration in revolutions per second per second. (b) Find the number of revolutions made by the fan blades during the time that they are slowing down in part A. (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

540 rev/min = 9 rev/sec

220 rev/min = 3.666 rev/sec

(a) using rotational kinematics

3.666 = 9 + a*3.85

a = -1.38528 rev/s² (negative sign is because fan is slowing down)

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(b) 3.666 ² = 9² + 2*a*

= 24.38

or

= 24 full revolutions

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(c) if fan comes to rest, then its final angular velocity is zero

0 = 9 + (-1.38528)t

t = 6.496 sec

therefore, fan will take 2.646 sec more