Physic Labs
Step 1 of 4: An isolated two-body system
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Intuition

Two skaters on smooth ice who only push each other — there is no 'third party' acting on them.

P⃗hệ=p⃗1+p⃗2=m1v⃗1+m2v⃗2\vec{P}_{\text{hệ}} = \vec{p}_1 + \vec{p}_2 = m_1\vec{v}_1 + m_2\vec{v}_2
Analysis

Consider a system of exactly two bodies with no external force, interacting only through F⃗12\vec{F}_{12} (body 1 on body 2) and F⃗21\vec{F}_{21} (body 2 on body 1). The total momentum of the system is the sum of the individual momenta.