L29 : Methods of momentum

Linear momentum of a particle is mass times the velocity of the particle. Linear momentum of a mass system is the vector sum of the linear momenta of all its particles. If we denote this linear momentum by G and mass and velocity of the ith particle by m_i and V_i  respectively, then

When the mass of each particle remains constant, the above expression may be written as

If r_G is the position vector of mass center and m is the total mass, then

Thus,

,where V_G  is the velocity of the mass center.