## A paradox inside Newtonian world

Yes because the force on the center of mass will be equal to the sum of the forces on all particles in the system. Thus the forces add to be infinite. This is a problem.
 First of all, the force to the mass center is NOT the sum of all forces. Not at all. Do you know that?

 Quote by Tomaz Kristan First of all, the force to the mass center is NOT the sum of all forces. Not at all. Do you know that?
$$M\mathbf{R} = \sum_i m_i \mathbf{r}_i$$
$$M\dot{\mathbf{R}} = \sum_i m_i \dot{\mathbf{r}_i}$$
$$M\ddot{\mathbf{R}} = \sum_i m_i \ddot{\mathbf{r}_i}$$