A high-speed flywheel in a motor is spinning at 500 rpm when a power failure sud

Question

A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 42.0 kg and diameter 73.0 cm . The power is off for 29.0 s and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 170 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?

Explanation / Answer

2* rad/revolution
60 seconds/min

170 revs=1068.14 rad

450 rpm= 52.35 rad/s

using

=0+0*t+0.5**t^2
0=0
0= 52.35
t=29
=1068.14
1068.14 =52.35*29+0.5**29^2
solve for
=0.550 rad/s

now that we have , we can solve for using

= 52.35-0.550*29
36.4 rad/sec
or
347.5 rpm


If the power had stayed off

0=52.35-0.550*t
solve for t
t=95seconds

and

= 52.35*95-0.5*0.550*95^2
2492 rad
or 397 revs

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