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 80.0 complete rotations. Assuming the frictional torque remains constant, how much more time N will it take the bike wheel to come to a complete stop? Number A27 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 tr that was acting on the spinning wheel. Give up & Vitre Soulion Q, check Answer 0 Ntxt Exit s Hint

Explanation / Answer

a)
wo = 9 rev/s

= 9*2*pi rad/s

= 56.5 rad/s

let alfa is the angular acceleration of the wheel.

angular displacement in first 10s, theta = 80 rotataions

= 80*2*pi radians

= 502.6 radians

theta = wo*t + (1/2)*alfa*t^2

502.6 = 56.5*10 + (1/2)*alfa*10^2

==> alfa = -1.248 rad/s^2

total time taken to stop, t = (wf - wo)/alfa

= (0 - 56.5)/(-1.248)

= 45.3 s

so, more time taken to stop = 45.3 - 10

= 35.3 s

b) Now use,

|Torque| = I*|alfa|

= m*r^2*alfa

= 0.725*0.315^2*1.248

= 0.0898 N.m

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