Is the Center of Mass an Abstraction?

In summary, the center of mass is an abstraction that does not necessarily lie within the rigid body itself. The internal forces add to zero at the center of mass and this is why objects tend to rotate around it. However, there are infinitely many points around the center of mass that have zero internal forces, making the argument that the center of mass is the only point where internal forces add up to zero flawed. There is also a theorem that states that the angular momentum around the center of mass behaves as if it is only being acted upon by external torques.
  • #1
aaaa202
1,169
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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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  • #2
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."
 
  • #3
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.
 
  • #4
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.
 
  • #5
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..
 

1. What is the center of mass?

The center of mass is a point in an object or system where the mass is evenly distributed in all directions. It is also known as the center of gravity.

2. How is the center of mass calculated?

The center of mass is calculated by finding the weighted average of the individual masses in an object or system. This can be done by multiplying each mass by its distance from a chosen reference point, and then dividing the total by the sum of all the masses.

3. Is the center of mass the same as the geometric center?

No, the center of mass and geometric center are not always the same. The geometric center is the point where an object would balance on a pivot, while the center of mass takes into account the distribution of mass within an object.

4. Why is the center of mass important in physics?

The center of mass is important in physics because it helps to describe the overall motion of an object or system. It can also be used to determine the stability of an object and how it will behave when subjected to external forces.

5. Is the center of mass an abstraction?

Yes, the center of mass is an abstraction because it is a theoretical concept used to simplify the analysis of complex systems. It does not physically exist in an object, but it is a useful tool in understanding its motion and behavior.

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