A flywheel in a motor is spinning at 530rpm when a power failure suddenly occurs

Question

A flywheel in a motor is spinning at 530rpm when a power failure suddenly occurs. The flywheel has mass 40.0kg and diameter 75.0cm . The power is off for 40.0s , and during this time the flywheel slows down uniformly due to friction in its axle bearings. During the time the power is off, the flywheel makes 250 complete revolutions.

At what rate is the flywheel spinning when the power comes back on?
w(omega)=___rpm

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, and how many revolutions would the wheel have made during this time?
t= ___s

N= ___rev

Please work your magic thank you so much!

Explanation / Answer

done the same question with different values The flywheel has mass 39.0 kg and diameter 78.0 cm. The power is off for 28.0 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 180 complete revolutions. At what rate is the flywheel spinning when the power comes back on? 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? sol:2*p rad/revolution 60 seconds/min 180 revs=1130.4 rad 450 rpm=47.1 rad/s using ?=?0+?0*t+0.5*a*t^2 ?0=0 ?0=47.1 t=28 ?=1130.4 1130.4=47.1*28+0.5*a*28^2 solve for a a=-0.4806 rad/s now that we have a, we can solve for ? using ?=47.1-0.4806*28 33.6432 rad/sec or 321.4 rpm If the power had stayed off 0=47.1-0.4806*t solve for t t=98 seconds and ?=47.1898*98-0.5*0.4806*98^2 2316.8 rad or 369 revs

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