# Dynamics of rigid bodies physics

• kyin01
In summary, the situation is like this: a ruler is pinned to a nail through its center, and has very little friction. Initially, the ruler is at rest and is sitting perfectly horizontal. I slightly push down on the right end of the ruler with my hand, and 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? The answer is that the equilibrium position is up/down, not only left/right. Thanks it really helped!

#### 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?

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!

## What is the definition of "rigid body" in physics?

A rigid body is a theoretical construct used in physics to describe an object that is assumed to have a perfectly rigid structure and does not deform under the influence of external forces.

## What is the difference between translational and rotational motion in rigid bodies?

Translational motion refers to the movement of a rigid body in a straight line, while rotational motion refers to the rotation of a rigid body around a fixed axis.

## What is the formula for calculating the moment of inertia of a rigid body?

The moment of inertia of a rigid body is calculated using the formula I = ∫ r² dm, where r is the distance from the axis of rotation and dm is the mass element of the body.

## How do external forces affect the motion of a rigid body?

External forces, such as gravity or applied forces, can cause a rigid body to accelerate or rotate. The resulting motion can be described using Newton's laws of motion and the principles of conservation of momentum and energy.

## Can a rigid body ever truly be perfectly rigid?

No, in reality, all objects have some degree of flexibility and can deform under the influence of external forces. However, the concept of a rigid body is useful in simplifying the analysis of motion in physics.