This is attempt to address Arcon's page on(adsbygoogle = window.adsbygoogle || []).push({});

center of mass

He says: [tex]\vec{R}=\frac{\sum m_i\vec{r_i}}{M}[/tex]

R is radius vector of the center;

r_{i}are radius vectors of m_{i};

M is sum of all m_{i};

It can be generalized to vector mass too.

[tex]M\vec{R}=M\vec{e_M}\times\vec{R}\times\vec{e_M}=\vec{M}\times\vec{R}\times\vec{e_m}[/tex];

also just like

[tex]\vec{M}=\sum \vec{m_i}[/tex]

under special conditions it can as well be

[tex]\vec{R}=\sum \vec{r_i}[/tex]

=> [tex](\sum \vec{r_i})\times(\sum \vec{m_i})=\sum (\vec{r_i}\times\vec{m_i})[/tex];

=> [tex]\sum_{i<>j} (\vec{r_i}\times\vec{m_j})=\vec{o}[/tex];

This way the position of the last mass depends on all the masses (including its own) and all the other positions;

I just can't say what are the terms for the last equation.

Can you?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The center of mass->

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**