Angular momentum for a system of particles:

Let us consider a system of n particles of masses \( m_1 \), \( m_2 \), \( \cdots \), \( m_n \) having position vectors \( \vec{r_1} \), \( \vec{r_2} \), \( \cdots \), \( \vec{r_n} \) respectively with respect to the origin O, whose velocities are \( \vec{v_1} \), \( \vec{v_2} \), \( \cdots \), \( \vec{v_n} \) respectively.

So the angular momentum of the system about the origin O is given by,

\( \vec{L}=\displaystyle{\sum_{i=1}^{n}}(\vec{r_i}\times{m_i\vec{v_i}}) \)

or, \( \vec{L}=\displaystyle{\sum_{i=1}^{n}}m_i(\vec{r_i}\times\vec{v_i}) \)

where, \( \vec{r_i} \) be the position vector of the ith particle of mass \( m_i \), whose velocity is \( \vec{v_i} \).