A student holds a bike wheel and starts it spinning with an initial angular spee
ID: 2245053 • Letter: A
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.
a) Assuming the frictional torque remains constant, how much more time ?ts will it take the bike wheel to come to a complete stop?
b) The bike wheel has a mass of 0.625 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 ?(f) that was acting on the spinning wheel.
Explanation / Answer
As we know that
theta = w0t + 0.5*alpha*t^2
(80*2pi) = (9*2pi)*10 + 0.5*alpha*10^2
alpha = - 1.25664 rad/sec^2
As we know
w = w0 + alpha*t
Therefore
0 = (9*2pi) - 1.25664*t
t = 45 sec
Frictional Torque = I*alpha
= (MR^2)*alpha
= (0.625*0.385^2)*1.25664
= 0.1164 Nm
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