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centre of mass

Posted: Wed May 02, 2007 5:24 am
by kolahalb
Prove that centre of mass is a unique point

I started with O as origin.G as CM and G' as assumed 2nd CM in the same sysyem of particles.

OG=R=(1/M) sum(i) [m_i*r_i]

OG'=R'=(1/M) sum(k) [m_k*r'_k]

The problem is theere is no unique relation between r_i and r'_k

Posted: Wed May 02, 2007 12:28 pm
by twistor
r_i and r'_k locate the particle in the coordinate system. Since you're using the same coordinate system to describe supposedly 2 different centers of mass, it must be that r_i = r'_k. This is because OG and OG' are the same coordinate system (remember, you're describing two centers of mass in the same system. The result you seek follows immediately.