kaw of conservation of linear momebtum
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The law of conservation of momentum states that for two objects colliding in an isolated system, the total momentum before and after the collision is equal.
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We know that the linear momentum of the particle is
p = mv
Newton’s second law for a single particle is given by,
F = dPdt
where F is the force of the particle. For ‘ n ‘ no. of particles total linear momentum is,
P = p1 + p2 +…..+pn
each of momentum is written as m1 v1 + m2v2 + ………..+mnvn. We know that velocity of the centre of mass is V = Σ miviM,
mv = Σ mivi
So comparing these equations we get,
P = M V
Therefore we can say that the total linear momentum of a system of particles is equal to the product of the total mass of the system and the velocity of its center of mass. Differentiating the above equation we get,
dPdt = M dVdt = MA
dv/dt is acceleration of centre of mass, MA is the force external. So,
dPdt = Fext
This above equation is nothing but Newton’s second law to a system of particles. If the total external force acting on the system is zero,
Fext = 0 then, dPdt = 0
This means that P = constant. So whenever the total force acting on the system of a particle is equal to zero then the total linear momentum of the system is constant or conserved. This is nothing but the law of conservation of total linear momentum of a system of particles
p = mv
Newton’s second law for a single particle is given by,
F = dPdt
where F is the force of the particle. For ‘ n ‘ no. of particles total linear momentum is,
P = p1 + p2 +…..+pn
each of momentum is written as m1 v1 + m2v2 + ………..+mnvn. We know that velocity of the centre of mass is V = Σ miviM,
mv = Σ mivi
So comparing these equations we get,
P = M V
Therefore we can say that the total linear momentum of a system of particles is equal to the product of the total mass of the system and the velocity of its center of mass. Differentiating the above equation we get,
dPdt = M dVdt = MA
dv/dt is acceleration of centre of mass, MA is the force external. So,
dPdt = Fext
This above equation is nothing but Newton’s second law to a system of particles. If the total external force acting on the system is zero,
Fext = 0 then, dPdt = 0
This means that P = constant. So whenever the total force acting on the system of a particle is equal to zero then the total linear momentum of the system is constant or conserved. This is nothing but the law of conservation of total linear momentum of a system of particles
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