A high-speed flywheel in a motor is spinning at 500.0 rpm when a power failure s

Question

A high-speed flywheel in a motor is spinning at 500.0 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 75.0 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 200 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?

Please tell me if my work is right.

500.0 rpm= 8.333 rev/s, which is 0=52.36 rad/s

200rev= 1260 rad

A)

=0+0t+0.5t^2-> -0=0t+0.5t^2 -> =1260-(52.36*30.0)/(0.5*30.0^2) -> =-310.8/450 ->

= -0.691 rad/s^2

=0+t -> =52.36-(0.691*30.0) = 31.63 rad/s

B) =0+t -> 0=0+t -> t=-52.36/ -0.691 -> t=75.8 sec

C) =0+0+0.5t^2 -> =0+0+0.5t^2 -> =31.63*75.8+[0.5*(-0.691)*75.8^2] -> =412 rev

Explanation / Answer

Your work is correct except for the formulae of C), It should be

=0+*t+0.5t^2, Substitutions are correct.

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