- #1
Reshma
- 749
- 6
Prove that the magnitude of R of the position vector for the centre of mass from an arbitrary origin is given by the equation:
[tex]M^2R^2 = M\sum m_ir_i^2 - {1\over 2}\sum m_i m_j r_{ij}^2[/tex]
Well the centre of mass is given by:
[tex]\vec R = \frac{\sum m_i r_i}{M}[/tex]
But squaring this doesn't seem to produce the result I require. I need more help.
[tex]M^2R^2 = M\sum m_ir_i^2 - {1\over 2}\sum m_i m_j r_{ij}^2[/tex]
Well the centre of mass is given by:
[tex]\vec R = \frac{\sum m_i r_i}{M}[/tex]
But squaring this doesn't seem to produce the result I require. I need more help.