A high-speed flywheel in a motor is spinning at 450 rpm when a power failure suddenly occurs.?

Question

The flywheel has mass 39.0 kg and diameter 78.0 cm. The power is off for 28.0 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 on? How many revolutions would the wheel have made during this time?

Answer 1

2*π rad/revolution
60 seconds/min

180 revs=1130.4 rad

450 rpm=47.1 rad/s

using

θ=θ0+ω0*t+0.5*α*t^2
θ0=0
ω0=47.1
t=28
θ=1130.4
1130.4=47.1*28+0.5*α*28^2
solve for α
α=-0.4806 rad/s

now that we have α, we can solve for ω using

ω=47.1-0.4806*28
33.6432 rad/sec
or
321.4 rpm


If the power had stayed off

0=47.1-0.4806*t
solve for t
t=98 seconds

and

θ=47.1898*98-0.5*0.4806*98^2
2316.8 rad
or 369 revs

j

Answer 2

Flywheel Spinning