I bow to the immortal law of conservation of momentum but consider my argument below and see if you can disprove it:
Example 1: Momentum cannot be conserved during an inelastic collision. When two bodies undergoing inelastic collision, they loose kinetic energy which might go into heat, light etc. Consider the situation in which the kinetic energy goes into heat energy, speeding up the molecules of air, consequently increasing its temperature. (Thermodynamics tells us that during transfer of energy (heat), temperature rises because of increase in the movement of molecules.) This means molecules are moving faster than they were before the collision. So they must have been transferred some momentum from the two bodies.
Putting the whole story together: " In inelastic collision, momentum in not conserved since some energy is dissipated and so should the momentum be not the same all the time."
Due to the ambiguity in the above example, I have presented another one much better than the previous one:
Example 2: Consider an isolated system consisting of two bodies. They collide with each other inelastically and some kinetic energy is turned into vibrational energy of the atoms (of one of the bodies), causing a heating effect. Now in order for the vibrational energy to increase some momentum must have to be either gained or lost to those atoms. Isn't it? So, how should the momentum of two bodies be conserved without taking into account the momentum lost or gained to atoms of the two bodies?
I need to rule out this argument. Where am I wrong?
(Note: I am not asking you to prove that momentum remains conserved, I fully agree with it but rather to disprove my above argument.)