Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

Consider a system of \( n \) particles where the position vector of each particle relative to the centre of mass is \( \mathbf{r}'_i \). The value of the vector sum \( \sum_{i=1}^n m_i \mathbf{r}'_i \) is always:

1. \( M \mathbf{R} \), where \( M \) is total mass and \( \mathbf{R} \) is position of centre of mass
2. Dependent on the velocity of the centre of mass
3. Non-zero if external forces act on the system
4. \( \mathbf{0} \) (null vector)