Dynamics of rigid bodies physics

AI Thread Summary
When a ruler is pinned at its center and pushed down on one end, it will not return to its original horizontal position after the force is removed if the center of mass is perfectly aligned with the pivot point. Instead, it will remain at the position where it stops spinning, as the equilibrium position is determined by the center of mass being directly above the pivot. If the pivot is not at the center of mass, gravity will create a new equilibrium position. The discussion emphasizes that both horizontal and vertical balance must be considered for true equilibrium. Understanding these dynamics clarifies the behavior of rigid bodies in rotational motion.
kyin01
Messages
47
Reaction score
0
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?
 
Physics news on Phys.org
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!
 
Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
Back
Top