The principles of science, whose history can be traced back to centuries of presence in scientific writings and whose fidelity appears to have been verified through a variety of experiments and applications, could still need some corrections or even supplementary proposals so that their content becomes whole. The principle of energy conservation is at least two hundred years old and is one of the most undeniable principles, with universal application in classical and quantum physics. However, as we expand in this paper, dynamic energy could be defined more precisely by including cases that deviate from it. In other words, we highlight and fill a scientific gap relevant to the principle of energy conservation. Of course, this historical scientific principle cannot be restated. For scientific as well as pedagogical reasons, however, we highlight our findings and note the fields, both traditional and modern, of classical and quantum physics, that researchers must take into account to fully understand an object under study. We also introduce and apply the conservation of total mechanical energy in the cases of terminal velocity (falling object), and forced oscillation in classical mechanics as well as in the case of quantum mechanics.