Work, kinetic energy (KE), and potential energy (PE) are key physics concepts, taught in essentially every introductory physics course along with the physical laws such as the work-kinetic energy theorem and the conservation of mechanical energy, which describe how the values of those quantities change during various processes. Quite appropriately for introductory courses, little attention is paid to how those concepts play out when implemented via observations in reference frames moving with respect to each other.

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Editor’s note: See also the letter to the editor in this issue of TPT from
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Customarily, we describe quantities such as mass and electric charge that do not change under Galilean transformations as “invariants.” The term “covariant” is often used for laws that are form invariant under transformations among frames of reference. In this paper, we avoid that term since it is not needed and, if used, might cause confusion since it also denotes certain vector and tensor indices and certain kinds of derivatives in special and general relativity. The term is also linked to covariance in statistics.
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