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The center of mass->

  1. Jan 23, 2004 #1
    This is attempt to address Arcon's page on
    center of mass

    He says: [tex]\vec{R}=\frac{\sum m_i\vec{r_i}}{M}[/tex]
    R is radius vector of the center;
    ri are radius vectors of mi;
    M is sum of all mi;

    It can be generalized to vector mass too.

    [tex]M\vec{R}=M\vec{e_M}\times\vec{R}\times\vec{e_M}=\vec{M}\times\vec{R}\times\vec{e_m}[/tex];

    also just like
    [tex]\vec{M}=\sum \vec{m_i}[/tex]
    under special conditions it can as well be
    [tex]\vec{R}=\sum \vec{r_i}[/tex]

    => [tex](\sum \vec{r_i})\times(\sum \vec{m_i})=\sum (\vec{r_i}\times\vec{m_i})[/tex];

    => [tex]\sum_{i<>j} (\vec{r_i}\times\vec{m_j})=\vec{o}[/tex];

    This way the position of the last mass depends on all the masses (including its own) and all the other positions;

    I just can't say what are the terms for the last equation.
    Can you?
     
  2. jcsd
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