The integral int vec{r} dm = 0 for a homogene | vedclass

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(A) The position of the center of mass $\vec{R}$ of a system of particles is defined by the equation $\vec{R} = \frac{1}{M} \int \vec{r} dm$,where $M$

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Center of mass

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(A) The position of the center of mass $\vec{R}$ of a system of particles is defined by the equation $\vec{R} = \frac{1}{M} \int \vec{r} dm$,where $M$ is the total mass of the body.If we choose the origin of our coordinate system to be at the center of mass,then $\vec{R} = 0$.Substituting this into the definition,we get $0 = \frac{1}{M} \int \vec{r} dm$,which implies $\int \vec{r} dm = 0$.Therefore,the integral $\int \vec{r} dm$ is zero when the origin is at the center of mass of the body.

The integral $\int \vec{r} dm = 0$ for a homogeneous body is defined for which point?

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