A student holds a bike wheel and starts it spinning with an initial angular spee

Question

A student holds a bike wheel and starts it spinning with an initial angular speed of 9.0 rotations per second. The wheel is subject to some friction, so it gradually slows down. In the 10-s period following the inital spin, the bike wheel undergoes 77.5 complete rotations. Assuming the frictional torque remains constant, how much more time ts will it take the bike wheel to come to a complete stop? The bike wheel has a mass of 0.625 kg and a radius of 0.315 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque f that was acting on the spinning wheel.

Explanation / Answer

=ot-1/2t^2
=2(ot-)/t^2
o=2f=56.54 rad/s
t=10 s
=77.5*2=486.94 rad
then
=0.784rad/s^2
after 77.5 turns
=o-t
=56.54-0.784*10=48.7 rad/s
then the time to stop is given by
0=-t
t=/
t=48.7/0.784=62.11s

the frictional torque is given by
f=I=1/2mr^2
f=0.5*0.625*(0.315)^2*3.14
f=0.0973 Nm

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