The sum of moments of all the particles in a | vedclass

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(B) By definition,the position of the center of mass $\vec{R}_{cm}$ of a system of $n$ particles with masses $m_i$ at positions $\vec{r}_i$ is given b

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Zero

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(B) By definition,the position of the center of mass $\vec{R}_{cm}$ of a system of $n$ particles with masses $m_i$ at positions $\vec{r}_i$ is given by $\vec{R}_{cm} = \frac{\sum m_i \vec{r}_i}{\sum m_i}$.If we choose the center of mass as the origin,then $\vec{R}_{cm} = 0$,which implies $\sum m_i \vec{r}_i = 0$.The moment of a particle about the center of mass is defined as the product of its mass and its position vector relative to the center of mass,given by $m_i \vec{r}_i$.The sum of these moments for all particles in the system is $\sum m_i \vec{r}_i$.Since $\sum m_i \vec{r}_i = 0$ by the definition of the center of mass,the sum of the moments of all particles about the center of mass is always zero.

The sum of moments of all the particles in a system about its center of mass is always . . . . . .

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