# Homework Help: Distance from Center of Mass

1. Jun 3, 2014

### velo city

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' = -$\frac{m_{2}}{m_{1}+m_{2}}$r

and

r2' = $\frac{m_{1}}{m_{1}+m_{2}}$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 = $\frac{m_{1}r_{1}+m_{2}r_{2}}{m_{1}+m_{2}}$

3. The attempt at a solution

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2. Jun 3, 2014

### 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}