A high-speed flywheel in a motor is spinning at 450 rpmwhen a power failure sudd

Question

A high-speed flywheel in a motor is spinning at 450 rpmwhen a power failure suddenly occurs. The flywheel has mass 37.0 kg and diameter 71.0 cm . The power is off for 26.0 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? (in rad/sec)

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? (sec)

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

Explanation / Answer

i= 450 rpm = 47.12 rad/s

m=37kg

r=0.355m

t=26s

=180 rev= 180*2= 1131 rad

A)

= i*t+1/2t^2

1131 = 47.12*26 +1/2**26^2

Gives, = -0.28 rad/s^2

f = i + *t = 47.12 - 0.28*26 = 39.84 rad/s

B) When f = = rad/s

f = i + *t

0= 47.12 - 0.28*t

Gives, t= 168.29 s

C) = i*t+1/2t^2 = 47.12*168.29 +1/2*-0.28*168.29^2 = 3965 rad = 631 rev

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