Why is the symbol U often used to represent potential energy? This question came up recently in a faculty discussion.

Before you get too excited, this post won’t resolve the issue. However, the earliest use of the letter “U” for potential energy was in a paper from 1853 by William John Macquorn Rankine: “On the general law of the transformation of energy,” Proceedings of the Philosophical Society of Glasgow, vol. 3, no. 5, pages 276-280; reprinted in: (1) Philosophical Magazine, series 4, vol. 5, no. 30, pages 106-117 (February 1853). The wikipedia article on potential energy indicates that his article is the first reference to a modern sense of potential energy. Below is the original text (yellow highlighting mine). I think we will have to ask Bill Rankine why he chose the symbol “U”:

“Let U denote this potential energy.”
Thus spake Rankine.