Principle of Conservation of Momentum:

It may be observed from impulse momentum equation that when sum of the impulses due to external forces is zero, the momentum of any system remains constant or is conserved. A case of two masses, gun and a shell is a popular instance as a study case. Throughout an extremely small interval of explosion the forces F_{s (t )}  and F_{g (t )} acting on shell and the gun, respectively are equal at all given instant of time and opposite in direction. The sum-total of the impulse (F_{s(t )}  dt + F_{g (t)} dt) is thus, always zero. The sum-total of the change in momentum of shell and gun is also zero by virtue of the above referred equation. If m_s and m_g are masses of shell and gun respectively,

--------- (1)

                        m_s V_2s   +  m_g V_2g    =    m_s   V_1s       +      m_gV_1g

where, V_{1 s}  and V_{2 s} are the velocities of shell at time t₁ and t₂, and V_1g and V_2g are the velocities of gun at time t₁  and t₂ respectively.

Therefore, Eq. (1) is the statement of the principle of conservation of momentum.