Obtain Newton's second law for system of particle and write it.
Obtain Newton's second law for system of particle and write it.
Linear momentum of system of particle
$\vec{p}=m \vec{v}$
Taking differention on both side with time
$\frac{d \vec{p}}{d t}=\mathrm{M} \frac{d \vec{v}}{d t}$ (where $\mathrm{M}=$ constant $)$
$\therefore \frac{d \vec{p}}{d t}=\mathrm{MA}$
$\ldots$ (2)
but $\overrightarrow{\mathrm{MA}}=\overrightarrow{\mathrm{F}}_{\mathrm{ext}}$
From equation (2) and (3),
$\frac{d \vec{p}}{d t}=\overrightarrow{\mathrm{F}}_{\mathrm{ext}}$
is a Newton's second law for the system of particles.
"The external force acting on a system is equal to rate of change of total linear momentum of the system." This is Newton's second law for a system.
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