A student holds a bike wheel and starts it spinning with an initial angular spee
ID: 1787840 • Letter: A
Question
A student holds a bike wheel and starts it spinning with an initial angular speed of 9.0 rouaüons 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 will it take the bike wheel to come to a complete stop? constant, how much more time Number 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 pinning wheel. ting on the s Number N- mExplanation / Answer
Torque = I *
Since the mass of the wheel is assumed to be located on the rim, I = m * r^2
I = 0.725 * 0.315^2 = 0.071938125
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 = 9 * 2 = 18 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
= 80 * 2 = 160 radians
160 = 18 * 10 + ½ * * 100
160 – 180 = 50 *
= (160 – 180) ÷ 50 = -20/50 = -0.4
Now we can determine the torque.
Torque = Iw
Torque = 0.071938125 * -0.4
This is approximately -0.09 N-m
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 = 18 – 0.4 * 10
f = 14
Use the same equation to determine the time for the wheel to come to a complete stop.
0 = 14 – * t
t = 14 seconds
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