Question

A cooling fan is turned off when it is running at 810 rev/min . It turns 1000 revolutions before it comes to a stop. A) What was the fan's angular acceleration, assumed constant? B) How long did it take the fan to come to a complete stop?

      

Answer 1

given

wi = 810 rev/min

= 810*2*pi/60

= 84.82 rad/s

angular displacement, theta = 1000 revolutions

= 1000*2*pi radians

= 6283 radians

wf = 0

A)
let alfa is the constant angular acceleration.

use, alfa = (wf^2 - wi^2)/(2*theta)

= (0^2 - 84.82^2)/(2*6283)

= -0.57 rad/s^2 <<<<<<--------- Answer

B) time taken to stop, t = (wf - wi)/alfa

= (0 - 84.82)/(-0.57)

= 150 s <<<<<<--------- Answer

Answer 2

$w_{1}=810\frac{2\pi }{60}\frac{rads}{s}=27\pi$

$w_{2}=0$

$1000\: revs=2000\pi \: rads$

Acceleration:

$a=\frac{w^{2}}{2x}=\frac{(27\pi )^{2}}{2(2000\pi )}\rightarrow \boldsymbol{a=-0.57\frac{rad}{s^{2}}}$

Time:

$t=\frac{w}{a}=\frac{27\pi }{0.57}\rightarrow \boldsymbol{t=148.81s}$