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Distance from Center of Mass

  1. Jun 3, 2014 #1
    I have attached the image as an attachment

    1. The problem statement, all variables and given/known data

    I am reading a classical mechanics textbook and I don't understand how they found that.

    r1' = -[itex]\frac{m_{2}}{m_{1}+m_{2}}[/itex]r

    and

    r2' = [itex]\frac{m_{1}}{m_{1}+m_{2}}[/itex]r

    r1' is the vector from the center of mass R to m1 and r2' is the vector from the center of mass R to m2.




    2. Relevant equations

    Center of mass = [itex]\frac{m_{1}r_{1}+m_{2}r_{2}}{m_{1}+m_{2}}[/itex]

    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Jun 3, 2014 #2

    DrClaude

    User Avatar

    Staff: Mentor

    If the origin is at the center of mass (which it is for ##r_1'## and ##r_2'##) then by definition of the center of mass
    $$
    \sum_i m_i r_i = 0
    $$
    The distance between masses 1 and 2 being ##r \equiv r_2' - r_1'##, we have
    $$
    \begin{align}
    m_1 r_1' &= -m_2 r_2' \\
    m_1 r_1' &= -m_2 (r + r_1') \\
    r_1' (m_1 + m_2) &= - m_2 r \\
    r_1' &= -\frac{m_2}{m_1 + m_2} r
    \end{align}
    $$
     
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