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Law of Conservation of Linear Momentum

If no external force acts on a system (called isolated) of constant mass, the total momentum of the system remains constant with time.
  • According to this law, for a system of particles, 34041.png
    In the absence of external force, 34035.png, then 34029.png constant
    i.e., 34023.png constant
    or 34017.png constant (2)
    Equation (2) shows that in absence of external force for a closed system the linear momentum of individual particles may change but their sum remains unchanged with time.
  • Law of conservation of linear momentum is independent of the frame of reference though linear momentum depends on the frame of reference.
  • Conservation of linear momentum is equivalent to Newton’s third law of motion.
    For a system of two particles in absence of external force by law of conservation of linear momentum.
    34011.png constant.
    ∴ 34005.png constant.
    Differentiating above with respect to time,
    ⇒ 33991.png
    ⇒ 33984.png
    ∴ 33978.png
    i.e., for every action there is equal and opposite reaction which is Newton’s third law of motion.

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