Galilean invariance of the work-energy theorem

Galileo Galilei (1564‐1642)

In Special Relativity, physical laws are required to assume the same mathematical form in all inertial frames of reference. In other words, the laws must be Lorentz-invariant.

In classical (Newtonian) Mechanics the Lorentz transformations reduce to the much simpler Galilean transformations. Under the latter, the laws of Mechanics (but not those of Electromagnetism!) are invariant in form in order for them to be valid in all inertial frames of reference.

Now, since Newton's laws are valid in all inertial frames, this must also be the case with regard to every theorem derived from them. Perhaps the most important such theorem (since it is associated with the conservation of energy) is the work-energy theorem. Here is now a good exercise for the Physics student: Let us assume that the work-energy theorem is valid for a certain inertial observer O. Can we show that this theorem will then be valid for any other inertial observer O΄?

The mathematical proof is not trivial! It may be given as a Physics project to the student.

See the article...