A high-speed flywheel in a motor is spinning at 450 rpm when a power failure sud

Question

A high-speed flywheel in a motor is spinning at 450 rpm when a power failure suddenly occurs. The flywheel has mass 44.0 kg and diameter 74.0 cm . The power is off for 31.0 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 160 complete revolutions.

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?

How many revolutions would the wheel have made during this time?

Explanation / Answer

2* rad/revolution
60 seconds/min

160 revs=1005.30 rad

450 rpm=47.1 rad/s

using

=0+0*t+0.5**t^2
0=0
0=47.1
t=31
=1005.30
1005.30=47.1*31+0.5**31^2
solve for
=-0.9465 rad/s

now that we have , we can solve for using

=47.1-0.9465*31
17.75 rad/sec
or
169.50 rpm


If the power had stayed off

0=47.1-0.9465*t
solve for t
t=49.76 seconds

and

=47.1898*49.76-0.5*0.9465*49.76^2
1176.37 rad
or 187 rev

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