A student holds a bike wheel and starts it spinning with an initial angular spee
ID: 1509813 • Letter: A
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 Deltat_s will it take the bike wheel to come to a complete stop? Deltat_s = 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 tau_f that was acting on the spinning wheel. tau_f =Explanation / Answer
Torque = I *
Since the mass of the wheel is assumed to be located on the rim, I = m * r^2
I = 0.625 * 0.385^2 = 0.09264
To determine the angular acceleration, we need to determine the wheel’s angular velocity before and after rotating for 10 seconds. Let’s convert rotations per second to rad/s.
1 rotation = 2 radians
Initial angular velocity = 7 * 2 = 14 rad/s.
This is the wheel’s angular velocity before the friction force is applied. Use the following equation to determine the angular acceleration.
= i * t + ½ * * t^2
1 rotation = 2 radians
= 45 * 2 = 90 radians
90 = 14 * 10 + ½ * * 100
90 – 140 = 50 *
= (90 – 140) ÷ 50 = -50/50 = -
Now we can determine the torque.
Torque = 0.09264 * -
This is approximate -0.291
The torque is negative because it caused the angular velocity to decrease.
To determine the time for the wheel to come to a complete stop, we need to determine the wheel’s angular velocity after the 10 seconds. Use the following equation.
f = i + * t, i = 14 rad/s
f = 14 – * 10
f = 4
Use the same equation to determine the time for the wheel to come to a complete stop.
0 = 4 – * t
t = 4 seconds
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