Rotational and translational motion of a ruler on a pivot

AI Thread Summary
A ruler attached to a pivot point will continue to spin if the pivot is frictionless, regardless of the downward force applied being less than its weight. The applied force causes the ruler to rotate, but it will not detach from the pivot unless the force exceeds the ruler's weight. The motion of the ruler's center of mass remains unchanged during this process, as the center of mass does not experience a net force that would alter its trajectory. Even a small applied force can initiate motion, leading to perpetual spinning in the absence of friction. The discussion emphasizes the distinction between the ruler's rotational motion and the behavior of its center of mass.
paulsberardi
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Homework Statement


A ruler is attached to the top of a pole bound by its center (pivot point of the ruler is at its center). A student briefly exerts a downward force on the right end of the ruler. The magnitude of the force exerted by the student is less than the weight of the ruler. Assume that pivot point is frictionless.


Homework Equations


After the student stops pushing the ruler, will it continue spinning or come to a stop?
Does the motion of the ruler's center of mass ever change?

The Attempt at a Solution


I am assuming the ruler will spin forever if the pivot point is frictionless, but I wasn't sure because the force applied on it was less than its weight. That had me thinking of the possibility that the ruler's motion may change direction and it will be restored to its original position.
 
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I believe if the force is less than the weight of the ruler then the ruler wouldn't spin. It would rotate clockwise then counter-clockwise back to the resting position.
 
You are right that if there is no friction the ruler will continue spinning.

As for the second part, remember that there is a difference between the "ruler's motion" and the "motion of the ruler's center of mass".

Does this help?
 
@longball, the force exerted on the ruler will cause the ruler to spin even if it is much lighter than the ruler's weight. If the force was greater than the ruler's weight then the ruler could be "broken off" the pivot point. I think the point of the question was just to assume that the applied force was small compared to the weight of the ruler so that the ruler remains fixed at the pivot point.
 
Bacat said:
You are right that if there is no friction the ruler will continue spinning.

As for the second part, remember that there is a difference between the "ruler's motion" and the "motion of the ruler's center of mass".

Does this help?

Yes, so how will the motion of the ruler's center of mass change? And it doesn't matter how small the magnitude of the force applied is, it could still spin forever?
 

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