Question

A system of particles in motion has mass center G as shown in the figure. The particle i has mass $m_i$ and its position with respect to a fixed point O is given by the position vector ${\rho }_i$. The position of the particle with respect to g is given by the vector ${\rho }_i$. The time rate of change of the angular momentum of the system of particles about G is (The quantity $\ddot{{\rho }_i}$ indicates second derivative of ${\rho }_i$ with respect to time and likewise for $r_i$

• A. ${\Sigma }_i{r}_i\times m_i{\ddot{\rho }}_i$
• B. $\Sigma {\rho }_i\times m_i{\ddot{r}}_i$
• C. ${\Sigma }_i{r}_i\times m_i{\ddot{r}}_i$
• D. ${\Sigma }_i{\rho }_i\times m_i{\ddot{\rho }}_i$

Answer 1

The correct option is B $\Sigma {\rho }_i\times m_i{\ddot{r}}_i$

The time rate of change of the angular momentum of the system of particles about G is (The quantity $\ddot{{\rho }_i}$ indicates second derivative of ${\rho }_i$ with respect to time and likewise for $r_i$

$\Sigma {\rho }_i\times m_i{\ddot{r}}_i$