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 initial 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 tauf that was acting on the spinning wheel.

Explanation / Answer

9 rotations per second = 9*(2*pi) rad /sec = 9*(2*3.14) rad/sec

80 rotations = 80*2*3.14 radians

d = ut - 0.5*a*t^2

=> 80*2*3.14 = 9*(2*3.14)*10 - 0.5*a*10*10

=> a = 1.256 rad/sec^2

v = u -at

=> 0 = 9*(2*3.14) - 1.256*t

=> t = 45 sec

thus time required = 45-10 = 35 more seconds to stop

T = i*a

i = mr*2 = 0.725*0.315^2 = 0.071938125 km m^2

thus T = 0.071938125*1.256 = 0.090354285 N/m

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