Classical Linear Momentum

up:: 031 MOC Classical Mechanics

Given a particle of mass $m$ and velocity $\vec{v}$, its momentum is defined as

$$\vec{p}=m\vec{v}$$

When considering a system of particles, the total momentum is related to the Center of Mass, since

$$\vec{P}=\sum _i{m}_i{\vec{v}}_i=\sum _i{m}_i\frac{d{\vec{v}}_i}{dt}=\frac{d}{dt}\sum _i{m}_i\overrightarrow{r_i}=M\frac{d\vec{R}}{dt}$$

where $M$ is the total system’s mass and $\vec{R}$ is the center of mass.