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 .