Question

Verify that the law of conservation of linear momentum and kinetic energy is invariant under Galilean transformation.

Answer 1

Loss of kinetic energy does not imply momentum will not be conserved.

• Momentum will always be conserved in a two body collision (unless there is another body or a field which can take some of the momentum - even then, the total momentum will be conserved).
• Suppose two identical bodies with opposite velocities (hence, momentum are equal in magnitude and opposite in direction) collide and stick together.
• The whole kinetic energy is lost, but the momentum is conserved.