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 42.0 kg and diameter 77.0 cm . The power is off for 32.0 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 150 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?

t = ?

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

N = ?

Explanation / Answer

2* rad/revolution

60 seconds/min

180 revs=942.45 rad

450 rpm=47.1 rad/s

using

=0+0*t+0.5**t^2

0=0

0=47.1

t=28

=942.45

942.45=47.1*32+ 0.5**32^2

solve for

=-1.1030 rad/s

now that we have , we can solve for using

=47.1-1.1030*32

11.804 rad/sec

If the power had stayed off

0=47.1-1.1030*t

solve for t

t=42.70 seconds

and

=47.1*42.70-0.5*0.1.1030*42.70^2

= 1005.6255 rad

and

=47.1*42.70-0.5*0.1.1030*42.70^2

= 1005.6255 rad

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