Linear momentum is a product of the mass (m) of an object and the velocity (v) of the object. If an object has higher momentum, then it harder to stop it. The formula for linear momentum is p = mv. The total amount of momentum never changes, and this property is called conservation of momentum. Let us study more about Linear momentum and conservation of momentum.

Linear Momentum of System of Particles

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.