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Homework Help: Centre of mass is a unique point

  1. May 2, 2007 #1
    1. The problem statement, all variables and given/known data

    Prove that centre of mass is a unique point

    2. Relevant equations

    definition of CM

    3. 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
     
  2. jcsd
  3. May 2, 2007 #2

    mjsd

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    there will be a vector going from G to G'
     
  4. May 2, 2007 #3
    That is obvious.But how to show that?
     
  5. May 3, 2007 #4

    mjsd

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    Homework Helper

    I believe now you have a relation between [tex]r_i[/tex] and [tex]r'_i[/tex] for each i.
     
  6. May 3, 2007 #5
    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.
     
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