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State and prove the principle of conservation of linear momentum using Newtons second and third laws of motion.
Physics
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Statement of Conservation of Linear Momentum
In an isolated system (where no net external force acts), the total linear momentum of the system remains constant:
\vec{P}\text{total} = \text{constant}
Derivation using Newton's Laws:
Consider two interacting bodies A and B. Let FAB be the force exerted on A by B, and FBA be the force exerted on B by A. According to Newton's Third Law:
\vec{F}AB = -\vec{F}BA
According to Newton's Second Law:
\frac{d\vec{p}A}{dt} = -\frac{d\vec{p}B}{dt} ⇒ (d / dt)(\vec{p}A + \vec{p}B) = 0
\therefore \vec{p}A + \vec{p}B = \text{Constant}