Proving Magnitude of Position Vector for Centre of Mass

[metgt4]

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

M²R² = M\summ_ir_i² - (1/2)\summ_im_jr_ij²

Homework Equations

F = MR''

F = p'

p = \summ_jr_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'' = \frac{F}{M} = \frac{p&#039;}{M} = \frac{(\summ_jr_j&#039;)&#039;/M<br /> <br /> And that&#039;s about where I think I go wrong. Am I on the right path, or am I waaayyy off?

 

[kuruman]

We cannot see what you have done because your LateX code failed. Try re-posting and someone might be able to help you.