Question

while staring at your ceiling fan, you decide to study the rotation. You discover that the fan makes a complete revolution every 0.770s. When you turn the fan off, you find that it takes 65.0 s for it to come to rest. You then measure the blades and find the fan has a 1.10 m diameter.

A) Find the initail angular speed of the fan

B) Find the angular acceleration of the fan

C) Calculate the inear speed of the tip of teh blade 10.0 s after the fan was turned off.

D) Through how many revolutions does the fan turn while coming to a stop?

Answer 1

(A) No. of revolution per sec, w0 = 1 / 0.770 = 1.30

convert this in radian / s.

So, the initial angular speed w0 = (2*pi*1.30) = 8.17 rad/s

(B) speed after t = 65.0 s is ZERO.

use the expression -

w = w0 + alfa*t

=> 0 = 8.17 + alfa*65

=> alfa = -8.17 / 65 = -0.126 rad/s^2

(C) Speed of the fan after 10 sec -

w = 8.17 - 0.126*10 = 6.91 rad/s

radius of the fan = 1.10 / 2 = 0.55 m

so, linear speed of the tip of the fan after 10 s, v = w*r = 6.91*0.55 = 3.80 m/s

(D) use the expression -

w^2 = w0^2 + 2*alfa*theta

=> 0 = 8.17^2 - 2*0.126*theta

=> theta = 8.17^2 / (2*0.126) = 264.88 rad.

So, the no. of revolution made by the fan while coming to stop = 264.88 / (2*pi) = 42.2 revolutions.