Forest UCM Ch3 CoM

The Center of mass

Definiiton of the Center of Mass

The position [math]\displaystyle{ \vec R }[/math] of the center of mass is given by

[math]\displaystyle{ \vec{R} = \frac{\sum_i^N m_i \vec{r}_i}{\sum_i^N m_i} }[/math]

The center of mass is given as the sum of the position of each object in the system weighted by the objects mass.

For a rigid object the location of the center of mass is given by

[math]\displaystyle{ \vec{R} = \frac{1}{M} \int \vec{r} dm }[/math]

Forest_UCM_MnAM#Center_of_Mass