Dynamics of rigid bodies physics

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Discussion Overview

The discussion revolves around the dynamics of a ruler pinned at its center and the effects of applying a force to one end. Participants explore whether the ruler will return to its original horizontal position after the force is removed or if it will remain in its new position. The conversation touches on concepts of equilibrium, center of mass, and rotational dynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant describes a scenario where a ruler is pinned at its center and pushed down at one end, questioning the behavior of the ruler after the force is removed.
  • Another participant suggests that if the pivot point is not at the center of mass, there will be an equilibrium position when the center of mass is directly below the pivot due to gravitational forces.
  • A participant reflects on the condition where the center of mass is exactly at the pivot point, proposing that the ruler will remain at rest in whatever position it stops, regardless of being horizontal or vertical.
  • Further clarification is provided that equilibrium must also consider vertical positioning, not just horizontal balance.

Areas of Agreement / Disagreement

Participants express varying views on the conditions under which the ruler will return to its original position or remain at rest. There is no consensus on the outcome, as different scenarios regarding the center of mass and pivot point are discussed.

Contextual Notes

The discussion includes assumptions about the uniformity of the ruler's mass and the precision of the pivot point's placement, which may affect the conclusions drawn by participants.

Who May Find This Useful

This discussion may be of interest to those studying dynamics, particularly in the context of rigid body motion and equilibrium conditions in physics.

kyin01
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So the situation is like this a ruler (of uniform mass) is pinned to a nail through its center. The has very little friction so it will spin but come to a stop. Initially it is at rest and is sitting perfectly horizontal (so that means the center of mass is at the center of the ruler).

Now I slightly push down on the right end of the ruler with my hand.

The main question is, after I release my hand ( no more force) will the ruler return to its horizontal resting place it was initially at or will it just remain at the position where ever the spin stops?

This is confusing because when I try this at home with a ruler rotating about my pencil (pencil is through a hole in the middle of my ruler), the ruler always return to some equilibrium position.

However, when I think about it, I don't see any other forces that will make the ruler go back horizontally (due to the center of mass being at the center) after I remove my hand that was pushing down.

So what is going on here? And what's really suppose to happen with the ruler?
 
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Point is, if the fixed point is not exactly on the center of gravity of the ruler, there will be an equilibrium position when this center of gravity is exactly below the fixed point, due to gravity.
 
vanesch said:
Point is, if the fixed point is not exactly on the center of gravity of the ruler, there will be an equilibrium position when this center of gravity is exactly below the fixed point, due to gravity.

I see what you mean there. So that means given a perfect condition where the center of mass of the ruler is EXACTLY in the center point (point of rotation) so that means left side of ruler = right side of ruler in terms of mass, given those conditions no matter where the ruler stops spinning that's the spot it will remain at rest right? Even if its not horizontal or vertical under those conditions
 
kyin01 said:
I see what you mean there. So that means given a perfect condition where the center of mass of the ruler is EXACTLY in the center point (point of rotation) so that means left side of ruler = right side of ruler in terms of mass, given those conditions no matter where the ruler stops spinning that's the spot it will remain at rest right? Even if its not horizontal or vertical under those conditions

Yes, but the equilibrium has also to be "up/down", not only "left/right".
 
vanesch said:
Yes, but the equilibrium has also to be "up/down", not only "left/right".

Upper part of ruler and bottom part of ruler, ok I'll keep that in mind.

Thanks it really helped!
 

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