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- Homework Statement
- proof that the distribution of mass around the center of mass is = 0.

- Relevant Equations
- ∫Rdm = 0

hi guys

in the proof of the parallel axis theorem this equation is just put as it is as a definition of the center of mass :

$$\int[2(\vec{r_{o}}.\vec{r'})I-(\vec{r_{o}}⊗\vec{r'}+\vec{r'}⊗\vec{r_{0}})]dm = 0$$

is there is any proof for this definition ? and what is the approach for it

in the proof of the parallel axis theorem this equation is just put as it is as a definition of the center of mass :

$$\int[2(\vec{r_{o}}.\vec{r'})I-(\vec{r_{o}}⊗\vec{r'}+\vec{r'}⊗\vec{r_{0}})]dm = 0$$

is there is any proof for this definition ? and what is the approach for it

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