This study is focused on the concept and formalism of work done and potential energy on the very fundamental level. A detailed analysis of the incomplete presentations of the topics found a major misconception that precluded acknowledgement of existence of certain nonradial effects caused by classical radial/center-bound gravitational force fields is offered. Certain consequences of this and some related misconceptions are also discussed as well the adverse impact of these misconceptions on research on education, teaching and learning of these topics, and on the future development of physical and mathematical theories related to, or relying on, these topics. The most noticeable conclusion of this study is that a more complete and transparent mathematical approach to physics is needed in order to prevent generating similar misconception in the future theories of physics and mathematical sciences in general. A conclusion of importance to educators is that they cannot rely on research scientists anymore, but should evaluate the contents of topics presented to undergraduate and graduate students in order to recognize possible misconceptions and reformulate presentations of topics whose mathematical incompleteness might lead to cognitive conflicts. These conclusions, when generalized, provide specific guidelines for educators, and especially for academic teachers, curriculum designers and researchers on issues pertinent to education. This study is not dealing with misconceptions created by students. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]