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.

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 80.0 complete rotations. Assuming the frictional torque remains constant, how much more time Deltats will it take the bike wheel to come to a complete stop? The bike wheel has a mass of 0.725 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 Tf that was acting on the spinning wheel.

Explanation / Answer

w0= 9rotation/s

time(t)=10s

no. of rotation(r)=80

let angular accelartion is a.

So, r = w0*t- 0.5*a*t^2

SOlving this, we have a=0.2 rotation/s^2

when it comes to stop w=0

a)SO, time taken = w0/a = 9/0.2 = 45s.

hence delta t =45-10 =35s

b) torque = Ia (where I is moment of inertia= mr^2)

=mr^2*a

=0.725*0.315^2*0.2 Nm

=0.014 Nm

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