I need all parts please A high-speed flywheel in a motor is spinning at 500 rpm

Question

I need all parts please

A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 42.0 kg and diameter 79.0 cm. The power is off for 30.0 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 or How many revolutions would the wheel have made during this time?

Explanation / Answer

initial angular velocity is wi = 500 rpm = (500*2*3.142)/60 = 52.4 rad/s

moment of inertia of fly wheel is I = 0.5*M*R^2 = 0.5*42*(0.79/2)^2 = 3.3 kg-m^2

angular displacement is theta = 180*2*3.142 = 1131.12 rad

time taken is t = 30 sec

A) angular accelaration is alpha

using theta = (wi*t) + (0.5*alpha*t^2)

1131.12 = (52.4*30)+(0.5*alpha*30^2)

alpha = -0.979 rad/s^2

then final angular velocity wf = wi + (alpha*t) = 52.4-(0.979*30) = 23 rad/s

B) if wf = 0 rad/s

then wf = wi + (alpha*t)

0 = 52.4-(0.979*t)

t = 53.5 sec

C) theta = (wi*t) + (0.5*alpha*t^2)

theta = (52.4*53.5)-(0.5*0.979*53.5^2) = 1402.32 rad/

No.of revolutions are 1402.3/(2*3.142) = 223 rev

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