A high-speed flywheel in a motor is spinning at 450 rpm when a power failure sud

Question

A high-speed flywheel in a motor is spinning at 450 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 72.0 cm. The power is off for 35.0 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

A.) At what rate is the flywheel spinning when the power comes back on?
= ? rad/s

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?
= ? s

C.) How many revolutions would the wheel have made during this time?
= ? rev

Explanation / Answer

The initial angular speed is 450 rpm wich is 47.1 rad/s

Part A)

Using = [(f + o)/2]t, we can find the final angular velocity

= 180 rev; since there are 2 rad per rev, that is 1131 rad

1131 = [[f + (47.1)]/2]35

f = 17.5 rad/s

Part B)

From the value found in part a, we can find the angular deceleration. Using...

f2 = o2 + 2

(17.5)2 = (47.1)2 + 2(1131)

= -.845 rad/s2

Then, f = o + t

(0) = (47.1) + (-.845)t

t = 55.7 sec

Part C)

Using f2 = o2 + 2, we have

(0) = (47.1)2 + 2(-.845)

= 1313 rad

Since there are 2 rad per rev, we can find the revs

1313/2 = 209 rev

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