Finding the Center of Mass for a Group of Masses

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Discussion Overview

The discussion revolves around the concept of finding the center of mass for a group of masses. Participants explore definitions, mathematical expressions, and conceptual understanding related to the center of mass in both rigid bodies and distributed masses.

Discussion Character

  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant inquires about the method to find the center of mass for multiple masses and suggests a possible connection to test masses and force directions.
  • Another participant requests a definition of the center of mass, prompting a reference to external sources.
  • A participant provides a definition from a wiki source, explaining that the center of mass is the average location of all mass in a system, noting its fixed position in rigid bodies versus its potential location in free space for distributed masses.
  • Further clarification is offered that the center of mass can be mathematically expressed, inviting participants to engage with the mathematical formulation.
  • One participant acknowledges missing the provided link to the definition and expresses gratitude for the clarification.

Areas of Agreement / Disagreement

Participants generally agree on the definition of the center of mass, but the method for calculating it and the implications of different mass distributions remain less clear and are not fully resolved.

Contextual Notes

The discussion does not delve into specific mathematical steps or assumptions required for calculating the center of mass, leaving those aspects unresolved.

Bread18
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Lets say I have n number of masses, x1, x2, x3,...,xn.

How do I find the center of mass of the group of masses? I'm not really sure how to do this, but does it have something to do with having a test mass and finding the direction of the force and different points around the group of masses, and then finding where they intersect? (I'm not sure what maths this would involve too.)

This isn't a homework question, I'm just curious as to how this can be done.
 
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According to wiki:
In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body. In the case of a loose distribution of masses in free space, such as shot from a shotgun or the planets of the Solar System, the position of the center of mass is a point in space among them that may not correspond to the position of any individual mass.
 
Bread18 said:
In physics, the center of mass ... is the average location of all of its mass.
That's what you need. Now express that mathematically. (See the link I gave.)
 
Oh, I missed that link lol, sorry.
 
Ok, thank you.
 

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