# Center of mass

1. Feb 16, 2012

### aaaa202

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..

2. Feb 16, 2012

### fluidistic

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. Feb 17, 2012

### aaaa202

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. Feb 17, 2012

### fluidistic

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. Feb 17, 2012

### aaaa202

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..