A flywheel in a motor is spinning at 520rpm when a power failure suddenly occurs

Question

A flywheel in a motor is spinning at 520rpm when a power failure suddenly occurs. The flywheel has mass 40.0kg and diameter 75.0cm . The power is off for 35.0s , and during this time the flywheel slows down uniformly due to friction in its axle bearings. During the time the power is off, the flywheel makes 240 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, and how many revolutions would the wheel have made during this time?

Part C

N=

Explanation / Answer

Here,

initial angular speed , wi = 520 rpm

wi = 54.44 rad/s

Using second equation of motion

240 * 2pi = 54.44 * 35 + 0.5 * a *35^2

a = -0.65 rad/s^2

Using third equaiton of motion

wf^2 - 54.44^2 = -2*240 * 2pi*0.65

solving for wf

wf = 31.67 rad/s

wf = 302.5 rpm

the final speed angular speed is 302.5 rpm

b)

Now, if the power doesn't come back up

using first equation of motion

54.44 = 0.65* t

t = 83.8 s

the time taken is 83.8 s

c)

Using second equation of motion

theta = 0.5 * 0.65 * 83.8^2

theta = 2279.8 rad

N = 2279.8/2pi = 362.9 rev

the number of rev is 362.9

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