Linear Momentum of System of Particles o
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The total momentum of a system of particles is equal to the product of the total mass of the system and the velocity of its COM.
P = p1 + p2 + …. + pn o
= m1v1 + m2v2 + …. + mnvn P = MV
Where o pi = momentum of i th particle, o P = momentum of system of particles, o
V = velocity of COM
o Newton’ s Second Law extended to system of particles: dP / dt = Fext. o
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When the total external force acting on a system of particles is zero( Fext = 0), the total linear momentum of the system is constant( dP / dt = 0 => P = constant). Also the velocity of the centre of mass remains constant( Since P = mv = Constant).
If the total external force on a body is zero, then internal forces can cause complex trajectories of individual particles but the COM moves with a constant velocity.
Example: Decay of Ra atom into He atom & Rn Atom
Case I – If Ra atom was initially at rest, He atom and Rn atom will have opposite direction of velocity, but the COM will remain at rest.