A paradox inside Newtonian world

nealh149

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.

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?

ObsessiveMathsFreak

It hadn't occurred to us.

[tex]M\mathbf{R} = \sum_i m_i \mathbf{r}_i[/tex]
[tex]M\dot{\mathbf{R}} = \sum_i m_i \dot{\mathbf{r}_i}[/tex]
[tex]M\ddot{\mathbf{R}} = \sum_i m_i \ddot{\mathbf{r}_i}[/tex]

Tomaz Kristan

Do you know, that this is not the case?

You and I could be forced to accelerate in the opposite directions, yet the center of the mass of the you&me system, would not move at all. Let alone to be accelerated.

Just one example.

ZapperZ

This thread has gone long enough, and I believe that nothing has been achieved. This topic is now closed, and no new ones should be opened related to it.

Zz.