Centre of mass is a unique point

Click For Summary

Homework Help Overview

The discussion revolves around proving that the center of mass (CM) is a unique point within a system of particles, focusing on the definitions and relationships involved in determining the CM.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between different assumed centers of mass and question how to demonstrate the uniqueness of the CM. There is discussion about the implications of having multiple centers of mass and the potential contradictions that arise from such a scenario.

Discussion Status

Some participants have made progress in identifying relationships between the positions of particles and their contributions to the center of mass. There is an acknowledgment of the contradiction that arises if multiple centers of mass are assumed, suggesting a productive direction in the discussion.

Contextual Notes

Participants are working under the assumption that the definition of center of mass applies uniformly across the system, and they are exploring the implications of this definition on the uniqueness of the CM.

neelakash
Messages
491
Reaction score
1

Homework Statement



Prove that centre of mass is a unique point

Homework Equations



definition of CM

The Attempt at a Solution



I started with O as origin.G as CM and G' as assumed 2nd CM in the same sysyem of particles.

OG=R=(1/M) sum(i) [m_i*r_i]

OG'=R'=(1/M) sum(k) [m_k*r'_k]

The problem is theere is no unique relation between r_i and r'_k
 
Physics news on Phys.org
there will be a vector going from G to G'
 
That is obvious.But how to show that?
 
I believe now you have a relation between [tex]r_i[/tex] and [tex]r'_i[/tex] for each i.
 
OK,I found it.R_CM is a function of (m_i,r_i).So, it has a unique value.

Another way to look at it:Suppose,there are exactly x(>1) CMs.Then you can show there are atleast x+1 CMs.So,it is a contradiction.
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
1K
Replies
16
Views
2K
Replies
1
Views
1K
  • · Replies 4 ·
Replies
4
Views
4K
Replies
13
Views
2K
Replies
8
Views
1K
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K