# Center of mass invariance

1. Sep 30, 2015

### HMT

Hi! I have been reading about the position of the center of mass in the Marion's Classical Dynamics book, in some point of the section he states that: "The location of center of mass of a body in uniquely defined, but the position vector R(of the center of mass ofcourse) depends on the coordinate system chosen". My query is: If we need a coordinate system to dermine the position of center of mass, how can I determine "just" the center of mass? What is Marion trying to say?

2. Sep 30, 2015

### Staff: Mentor

Not sure what you mean. You want to specify the center of mass without using a coordinate system?

3. Sep 30, 2015

### HMT

In fact this is my doubt. Are the location of center of mass & position vector of the center of mass the same thing?

4. Sep 30, 2015

### Staff: Mentor

Yes, I would say so. The position vector (of anything) specifies its location.

5. Sep 30, 2015

### HMT

But when Marion says : "The location of center of mass of a body in uniquely defined..." Is trying to say that there is only one center of massin one body?

6. Sep 30, 2015

### Staff: Mentor

That's right. And, of course, the location of that unique point can be specified using a position vector.

7. Sep 30, 2015

### HMT

I think I get it, perhaps It was a language confusion (english is not my idiom); anyway thank you! Regards

8. Oct 1, 2015

### vanhees71

This is a bit misleading, because a vector does not depend on the basis chosen, but of course its components do. Of course, the position vector depends on the choice of the origin of your frame. For a rigid body usually you even work with two frames, namely an inertial frame and a non-inertial frame fixed in the body.

9. Oct 1, 2015

### Staff: Mentor

Good clarification.

I think that was the issue here.

10. Oct 1, 2015

### mathman

The main point is the center of mass physically is independent of the coordinate system. For example, if the object (constant density) is shaped like a cylinder, the center of mass is in the center of the cylinder no matter how you set up the coordinate system.