- #1

metgt4

- 35

- 0

## Homework Statement

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}

## Homework Equations

F = MR''

F = p'

p = [tex]\sum[/tex]m

_{j}r

_{j}'

## 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?