How is the center of mass determined independently of the coordinate system?

[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?

Thanks for reading my doubt.

 

[Doc Al]

how can I determine "just" the center of mass?

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

 

[HMT]

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

 

[Doc Al]

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

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

 

[HMT]

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

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?

 

[Doc Al]

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?

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

 

[HMT]

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

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

 

[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.

 

[Doc Al]

This is a bit misleading, because a vector does not depend on the basis chosen, but of course its components do.

Good clarification.

Of course, the position vector depends on the choice of the origin of your frame.

I think that was the issue here.

 

[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.