# proof of the property related to center of mass.

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Prove the following statement:

"THE SUMMATION OF MASS MOMENTS OF ALL THE COMPONENTS OF SYSTEM ABOUT ITS CENTRE OF MASS IS ALWAYS EQUAL TO ZERO."

Closed as per community consensus as the post is Not graudate-level physics
Isn't it a definition of the center of mass $\mathbf{R}_{\rm{CM}}=\sum_i m_i\mathbf{r}_i/M_{\rm{tot}}$? When $\mathbf{R}_{\rm{CM}}=0$ it means the sum of mass moments is zero.