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 7.0 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 45.0 complete rotations. Assuming the frictional torque remains constant, how much more time Delta t_s 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 0.385 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque tau_f that was acting on the spinning wheel.

Explanation / Answer

from the rotational kinematic equation

theta = w0t + 0.5*alpha*t^2

(45) = (7)*10 + 0.5*alpha*10^2

alpha = 45-70/50 = 0.5 rev/s^2

wf = wi + alpha t

0= 7+ ( 0.5) t

t = 14 s

change in time

del t = 14 s - 10 s = 4s

torque is T = I * apha = m r^2 * alpha = 0.725 kg ( 0.385 )^2 ( 0.5) ( 2 pi) = 0.337 N m

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