centre of mass

Posts: 21
Joined: Thu Jan 11, 2007 2:09 pm

centre of mass

Postby kolahalb » Wed May 02, 2007 5:24 am

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

User avatar
Posts: 1531
Joined: Thu Apr 13, 2006 2:47 pm

Postby twistor » Wed May 02, 2007 12:28 pm

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.

Return to “Problems, Solutions, and Discussion”

Who is online

Users browsing this forum: Bing [Bot] and 1 guest