Calculate Angular Acceleration of Cooling Fan | 850 rev/min to Stop

[vinny380]

Question: A cooling fan is turned off when it is running at 850 rev/min. It turns 1500 revolutions before it comes to a stop.
A. What is the fan's angular acceleration?
B. How long does it take for the fan to come to a stop?

I am pretty stumped with this question. I know that I have to use the equation a= omega (angular velocity)/ time ...and angular velocity= Change in theta/time ...but i am not sure how to go about the problem ...can anyone help?

 

[Euclid]

You said it: $$\alpha = \frac{\Delta \omega}{\Delta t}$$
Be careful though. 850rev/min is the frequency, NOT the angular velocity. But these are related by $$2\pi f = \omega$$.

 

[vinny380]

thanks Euclid ... so I got an angular velocity of 5340 rev/sec ...but how would I figure out the time since a= change in angular velocity/time

 

[vinny380]

i am really confused... i don't even know if i got the angular velocity right ... 5340 revolutions per second seems so much ...

?

 

[Euclid]

Firstly, angular velocity is in units of 1/s or rad/s, not rev/sec.

Secondly, sorry for misleading you, I read the question wrong. You want to use the equation:

$$2 \alpha \Delta \theta = \omega_f^2 - \omega_i^2$$

How many radians does 1500 revolutions correspond to?

 

[vinny380]

would 1500 revolutions = 3000 radians? or am i totally off

 

[vinny380]

i know that the acceleration must be negative ... considering wf=0 ... and -w1^squared= 2Atheta

 

[vinny380]

anyone there ?? please help!