Is the Center of Mass an Abstraction?

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Discussion Overview

The discussion centers on whether the center of mass is a concrete point on a body or merely an abstraction. Participants explore the implications of internal forces and their relation to the center of mass, considering examples such as hollow objects and the behavior of forces in these contexts.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants propose that the center of mass is an abstraction, noting that it may not necessarily be located within the physical body itself, as illustrated by examples like hollow spheres and bottles.
  • Others argue that internal forces add to zero at the center of mass, suggesting that this property is fundamental to understanding motion and rotation around this point.
  • A later reply questions the reasoning behind the assertion that internal forces always add to zero at the center of mass, indicating a potential misunderstanding of the concept.
  • One participant mentions Newton's third law in relation to the center of mass, suggesting that it is a fundamental principle that explains why objects tend to rotate around their center of mass.
  • Another participant challenges the argument that internal forces must add to zero at a specific point, suggesting that there are infinitely many points around the center of mass where internal forces can also be zero.
  • There is a mention of a theorem regarding angular momentum around the center of mass, which implies that it behaves as if only external torques are acting on it.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the center of mass, with no consensus reached on whether it is a concrete point or an abstraction. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

Some statements rely on specific interpretations of internal forces and their behavior in relation to the center of mass, which may depend on the definitions used. The discussion also touches on the implications of Newton's laws and the behavior of angular momentum, but these concepts are not universally agreed upon.

aaaa202
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Is the center of mass a concrete point on a body or an abstraction?

As far as I can see the internal forces all add to zero in the center of mass. But if you imagine that a body made up of n particles with a single particle located exactly in the coordinates of the center of mass, I can't see why the forces on that particular particle should always add to zero.

I'm getting something wrong..
 
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aaaa202 said:
Is the center of mass a concrete point on a body or an abstraction?

As far as I can see the internal forces all add to zero in the center of mass. But if you imagine that a body made up of n particles with a single particle located exactly in the coordinates of the center of mass, I can't see why the forces on that particular particle should always add to zero.

I'm getting something wrong..

It's an "abstraction". The center of mass of a rigid body isn't necessarily inside the rigid body itself. Examples: a hollow sphere of a thickness d. A glass. A bottle, etc.
I do not really understand why the following would be true: "the internal forces all add to zero in the center of mass."
 
Newtons third law? It's quite a fundamental thing I believe. Haven't you ever wondered why an object always tends to rotate around its cm? That's because the internal forces add to zero in this point.
 
aaaa202 said:
Newtons third law? It's quite a fundamental thing I believe. Haven't you ever wondered why an object always tends to rotate around its cm? That's because the internal forces add to zero in this point.
Take the case of a hollow sphere. Apply a torque for say 1 s, tangentially to its surface. I agree that the hollow sphere will start to rotate around its center of mass. However there are infinitely many points around the center of mass that have absolutely zero internal forces. Thus the argument that it's because all the internal forces add up to zero at a particular point make it the center of mass and make the obect rotating around "that point" is flawed.
 
Now, I think there is also a theorem that says the angular momentum around the cm acts as though it was only being acted on by external torques..
 

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