Proving Magnitude of Position Vector for Centre of Mass

AI Thread Summary
The discussion centers on proving the magnitude of the position vector for the center of mass using the equation M2R2 = M∑ri2 - (1/2)∑mi mjrij2. The user expresses uncertainty about how to approach the problem, starting with the equation F = MR''. They attempt to derive R'' but feel they may be going off track. The response highlights a failure in their LaTeX code, suggesting that reposting the work could facilitate better assistance. Clarity in mathematical representation is crucial for effective problem-solving in this context.
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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\summiri2 - (1/2)\summimjrij2

Homework Equations



F = MR''

F = p'

p = \summjrj'



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<sub>j</sub>r<sub>j</sub>&#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?
 
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We cannot see what you have done because your LateX code failed. Try re-posting and someone might be able to help you.
 

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