A high$-$speed flywheel in a motor is spinning at $500$ rpm

when a power failure suddenly occurs. The flywheel has mass $37\mathrm{.}0$ kg

and diameter $72\mathrm{.}0$ cm

$.$ The power is off for $33\mathrm{.}0$ 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. Part A$-$ At what rate is the flywheel spinning when the power comes back on$?$

Express your answer in radians per second. Part 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$?$

Express your answer in seconds. Part C$-$ How many revolutions would the wheel have made during this time?

Express your answer in revolutions.