Interacting Systems of Particles

For a system of N interacting particles,

where L = m v and

	Initial linear momentum of the system of particle
	Linear impulse on the system due to the external forces acting on the system during the time interval
	Final linear momentum of the system of particle

Note that the impulses of the internal forces cancel out when the linear impulse and momentum equations for each particle are added.

If the sum of the impulses of all the external forces acting on the various particles is zero, the linear momentum of the system of particles is conserved.

While the total momentum of colliding particles is conserved, their total energy is generally not conserved. Therefore, we generally use the impulse and momentum principle across a collision and the work and energy method before and after a collision.