A high-speed flywheel in a motor is spinning at 500 rpmwhen a power failure sudd

Question

A high-speed flywheel in a motor is spinning at 500 rpmwhen a power failure suddenly occurs. The flywheel has mass 35.0 kg and diameter 73.0 cm . The power is off for 27.0 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.

Part A

At what rate is the flywheel spinning when the power comes back on?

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?

Part C

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

Explanation / Answer

initial angular speed = wo = 500 rpm = 500*(2pi/60) = 52.35 rad/s

displacement = 180*2*pi rad

displacement = average velocity*time

180*2*pi = (52.35+w1)*27/2

w1 = 31.43 rad/s = 300 rpm <<-answer

B)

angular acceleration alpha = (w1-wo)/t = (31.43-52.35)/27 = -0.775 rad/s^2

final velocity w2 = 0

w2 = wo + alpha*T

0 = 52.35 - 0.775*T

T = 67.55 s <<<----answer

C)

theta = (w2+wo)*T/2

theta = 52.35*67.55/2 = 1768.12 rad

theta = 1768.12/2pi = 281.4 revolutions   <--------------answer

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