Is the Center of Mass an Abstraction?

AI Thread Summary
The discussion centers on whether the center of mass is a concrete point or an abstraction. Participants argue that while internal forces may sum to zero at the center of mass, this does not mean that the center is always a specific point within the body. Examples like hollow spheres illustrate that the center of mass can exist outside the physical structure. The conversation also touches on Newton's third law and the tendency of objects to rotate around their center of mass, questioning the validity of the argument that internal forces must always add to zero at this point. Ultimately, the nature of the center of mass remains a complex topic that blends physical reality with theoretical concepts.
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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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