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 45.0 kg and diameter 76.0 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?
C) How many revolutions would the wheel have made during this time?

Explanation / Answer

Use theta=wo*t-0.3*alpha*t^2 150*2*pi=500*2*pi*32/60-1/2*alpha*t^2 1.43rad.sec^2=@ w=wo-@*t w=500*2*pi/60-1.43*32 w=6.57rad/sec put w=0 for next two wo/@=t 36.59secsec=t wo^2/2*@=theta 152.48 revolution

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