To find the centre of mass of a rigid body,why is it not possible to know $\sum m_i \vec{r}_i$ for all the particles?
(N/A) rigid body is composed of a continuous distribution of matter,consisting of an effectively infinite number of particles.
Because the number of particles is infinite,it is physically impossible to measure or track the individual mass $m_i$ and position vector $\vec{r}_i$ for every single particle.
Therefore,instead of using a discrete summation $\sum m_i \vec{r}_i$,we use the method of integration $\int \vec{r} \, dm$ to determine the centre of mass for a continuous body.
Because the number of particles is infinite,it is physically impossible to measure or track the individual mass $m_i$ and position vector $\vec{r}_i$ for every single particle.
Therefore,instead of using a discrete summation $\sum m_i \vec{r}_i$,we use the method of integration $\int \vec{r} \, dm$ to determine the centre of mass for a continuous body.
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