Counter rotation theory problem

AI Thread Summary
The discussion revolves around the motion of a meter stick placed on two counter-rotating wheels, with one wheel rotating clockwise and the other counter-clockwise. The initial confusion stems from whether the stick will remain stationary, oscillate, or be displaced due to its off-center position. Experimentation suggests that when the stick is centered, it remains stationary, but when off-center, it tends to fall. The key takeaway is that the friction and the initial off-center placement influence the stick's motion, leading to the conclusion that it will likely be displaced to the right. Overall, the problem highlights the complexities of balancing forces and the effects of friction in rotational systems.
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Homework Statement


A meter stick rests on two counter-rotating wheels. The left wheel rotates clockwise while the right wheel rotates counter-clockwise. There is friction between the meterstick and each wheel. The meter stick begins off-center to the right. What is the resulting motion of the meter stick?

The Attempt at a Solution



Wouldn't the meter stick simply just not move because the two wheel velocity cancel one another? but I got it wrong.


would it be The stick will be sent off the wheels to the right?
because the stick was off-center to the right at first?

or would it be The stick will oscillate back and forth?
or Nothing can be said about the stick's motion?
or The stick will be sent off the wheels to the left?

I'm quite confused
 
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If the wheels rotated slowly the stick would be balanced between the wheels. Make the following to prove it to yourself,
 

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Spinnor said:
If the wheels rotated slowly the stick would be balanced between the wheels. Make the following to prove it to yourself,

i tried to do the experiment, but it simply won't work because when i put the ruler off-centered to the right the ruler keep falling. however, i tried to do it when the ruler is centered, and the result is that the ruler doesn't move anywhere if i rotate both of the wheels with same speed. which means that the ruler stays on the same spot, but again it's not the answer.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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