Question

A cooling fan is turned off when it is running at 840 rev/min . It turns 500 revolutions before it comes to a stop.

1.) What was the fan's angular acceleration, assumed constant?

2.) How long did it take the fan to come to a complete stop?

Answer 1

Initial rotational speed of the fan = N₁ = 840 rev/min

Initial angular speed of the fan = ₁

₁ = 87.965 rad/s

Final angular speed of the fan = ₂ = 0 rad/s (Comes to a stop)

Number of revolutions the fan makes before coming to a stop = n = 500 rev

Angle through which the fan rotates =

= 2n

= 2(500)

= 3141.59 rad

Angular acceleration of the fan =

₂² = ₁² + 2

(0)² = (87.965)² + 2(3141.59)

= -1.232 rad/s²

Negative as the fan is slowing down.

Time taken by the fan to come to a stop = T

₂ = ₁ + T

0 = 87.965 + (-1.232)T

T = 71.4 sec

1) Angular acceleration of the fan = -1.232 rad/s²

2) Time taken by the fan to come to a complete stop = 71.4 sec