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$$\sum$$m_ir_i² - (1/2)$$\sum$$m_im_jr_ij²

Homework Equations

F = MR''

F = p'

p = $$\sum$$m_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'' = $$\frac{F}{M}$$ = $$\frac{p'}{M}$$ = [tex]\frac{($$\sum$$m_jr_j')'/M<br /> <br /> And that's about where I think I go wrong. Am I on the right path, or am I waaayyy off?[/tex]

 

[kuruman]

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