Question

while staring at your ceiling fan, you decide to study the rotation. You discover that the...

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?

Homework Answers

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.

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