"...and why the physical aperture of a lens is larger to achieve the same F-stop (which is a ratio) for a longer focal length..."

Just to clarify Troy's excellent post, the size of the physical aperture doesn't appear in the f-stop calculation, but the diameter of the entrance pupil (the appearance of the aperture, as seen from in front of the lens) does. I'm sure that Troy knows that, and I hope that he doesn't mind me mentioning it.

Best,
Helen