\begin{equation} \vec{ \textbf{p}} = m \vec{ \textbf{v}} \qquad (\textnormal{Momentum}) \tag{9.1} \end{equation} \begin{equation} \vec{\textbf{p}} = \vec{\textbf{p}}_A + \vec{\textbf{p}}_B \, + \, . . . \, = m_A \, \vec{\textbf{v}}_A + m_B \, \vec{\textbf{v}}_B \, + \, ... \end{equation} \begin{equation} \sum \vec{\textbf{F}} = \frac{d \vec{\textbf{p}}}{dt} \qquad (\textnormal{Newton's second law}) \tag{9.2} \end{equation} \begin{equation} \sum \vec{\textbf{F}} = \frac{d (m \vec{\textbf{v}})}{dt} \end{equation} \begin{equation} \vec{\textbf{J}} = \Delta \vec{\textbf{p}} \qquad (\textnormal{Impulse}) \tag{9.3} \end{equation} \begin{equation} \Delta \vec{\textbf{p}} = \sum \vec{\textbf{F}} \Delta t \end{equation} \begin{equation} \vec{\textbf{J}} = \sum \vec{\textbf{F}} \, \Delta t = \int \sum \vec{\textbf{F}} \, dt \end{equation} \begin{equation} \vec{\textbf{r}}_{cm} = \frac{m_1 \, \vec{\textbf{r}}_1 \, + m_2 \, \vec{\textbf{r}}_2 \, + \, m_3 \, \vec{\textbf{r}}_3 \, + \, \, ...}{m_1 + m_2 + m_3 \, + \, ...} \qquad (\textnormal{Center of mass}) \tag{9.4} \end{equation} \begin{equation} M \, \vec{\textbf{v}}_{cm} = m_1 \, \vec{\textbf{v}}_1 \, + m_2 \, \vec{\textbf{v}}_2 \, + \, m_3 \, \vec{\textbf{v}}_3 \, + \, ... \, = \vec{\textbf{P}} \qquad (\textnormal{Momentum of center of mass}) \tag{9.5} \end{equation} \begin{equation} \sum \vec{\textbf{F}}_{ext} = M \vec{\textbf{a}_{cm}} \qquad (\textnormal{Collection of particles, net charge ~ 0}) \tag{9.6} \end{equation}
Next module Extended objects and rotational motion