The principle of conservation of momentum is that, for a system of interacting objects, the total momentum in a specified direction remains constant, as long as no external forces act on the system. So, when two objects collide, the total momentum before and after the collision is the same.

Although momentum and total energy in a system are both conserved, total kinetic energy may not be conserved:

  1. Perfectly elastic: total KE is also conserved.

Inelastic: total KE is not conserved. Energy is transformed into heat, sound and EPE when the object is deformed.  The principle of conservation of momentum still holds in 2 dimensions: in collisions and interactions, linear momentum is conserved in all directions. If an object moves horizontally and then collides with another stationary object:

In the x direction,  m1v_{0}= m1v1costheta1 + m2v2costheta2

In the y direction0 = m_{1}v_{1}sintheta_{1} + m_{2}v_{2}sintheta_{2}