# Dynamics of rigid bodies

1. May 14, 2008

### kyin01

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?

2. May 14, 2008

### vanesch

Staff Emeritus
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.

3. May 14, 2008

### kyin01

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

4. May 14, 2008

### vanesch

Staff Emeritus
Yes, but the equilibrium has also to be "up/down", not only "left/right".

5. May 14, 2008

### kyin01

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

Thanks it really helped!