(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the magnitude R of the position vector for the centre of mass from an arbitrary origin is given by the equation

M^{2}R^{2}= M[tex]\sum[/tex]m_{i}r_{i}^{2}- (1/2)[tex]\sum[/tex]m_{i}m_{j}r_{ij}^{2}

2. Relevant equations

F = MR''

F = p'

p = [tex]\sum[/tex]m_{j}r_{j}'

3. The attempt at a solution

I'm not quite sure where to start with this, but this is what I've tried so far:

F = MR''

R'' = [tex]\frac{F}{M}[/tex] = [tex]\frac{p'}{M}[/tex] = [tex]\frac{([tex]\sum[/tex]m_{j}r_{j}')'/M

And that's about where I think I go wrong. Am I on the right path, or am I waaayyy off?

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# Center of Mass

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