Flywheel slows due to friction in its axle bearings

[azila]

Homework Statement

A high speed flywheel in a motor is spinning at 450 rpm when a power failure suddenly occurs. The flywheel has mass 35.0 kg and diameter 74.0 cm. The power is off for 33.0 seconds and during this time the flywheel slows due to friction in its axle bearings. During the time the power was off, the flywheel makes 180 complete revolutions.

a. at what rate is the flywheel spinning when the power comes back on.

b. how long after the beginning of the power failure would it have taken the flywheel to stop if the power had not come back on?

c. how many revolutions would the wheel have made during this time?

Homework Equations

so i was using the conversions of rev/min to rad/s for part a.

The Attempt at a Solution

i did this:
(180rev/33 sec)*(2*3.14 rad/ 1 rev)=34.3 rad/s
that is not the answer. So, I am guessing there is a bigger formula involved that I am missing.
Please help, thanks in advance.

 

[Hurkyl]

What quantity does (180rev/33 sec) compute?

 

[azila]

5.45 rev/sec

 

[azila]

i did that because that is how many revolutions per second that happened in the time the flywheel was not working, so...I did 180 (the amount of the revolutions that occurred during the time period the flywheel was off) over the time period the flywheel was down...I don't know if its right.

 

[azila]

I was just wondering, could this be done. Like the original rpm, is 450 rpm so convert that to rad/s. So, the original angular velocity is 52.4 rad/s and the angular velocity when the flywheel has power failure is 41.89 rad/s and t = 30s. So, I then did this:
.5 (41.89rad/s + 52.4 rad/s)(30) but the answer was way too huge. Is there something that I am missing or is this not the route to take? thanks for any help. and thanks for replying Hurkyl.

 

[Hurkyl]

I was just wondering, could this be done. Like the original rpm, is 450 rpm so convert that to rad/s. So, the original angular velocity is 52.4 rad/s and the angular velocity when the flywheel has power failure is 41.89 rad/s and t = 30s. So, I then did this:
.5 (41.89rad/s + 52.4 rad/s)(30) but the answer was way too huge. Is there something that I am missing or is this not the route to take? thanks for any help. and thanks for replying Hurkyl.

So you computed the (initial) angular velocty of the flywheel at the time when the power went off...

And then you computed the average angular velocity of the flywheel over the time between when the power went off and when the power went on...

And then you were trying to use this information to compute the (final) angular velocity of the flywheel at the time when the power went on...

Is that right?


(p.s. I deleted my previous post because I didn't think it was relevant after I saw your later post. I can usually manage to do that before anyone sees. :tongue2:)

 

[azila]

that's what i was trying to do, but I don't know if that's right?I am so confused. Am I even near on how to get the answer?

 

[Ahmed Abdullah]

This formula is applicable when angular acceleration is constant:
(Wi+Wf)/2=W ---------------(1)
Wi=intial angular velocity
Wf = final angular velocity
W=average angular velocity =angular distance (theta)/time

from (1) you can find Wf, which solve a.

#find angular acceleration and moment of inertia of the wheel
#then use relevant forumulas to solve (b) and (c)

 

[azila]

thanks for all the help, I finally figured out what I was doing wrong. I got it to work and I figured out the answer. Thanks everybody.