> My point is that I with kore than a decade of working theoretical physics I have NEVER seen anyone, student, professor or otherwise not use revolutions as the

> My point is that I with kore than a decade of working theoretical physics I have NEVER seen anyone, student, professor or otherwise not use revolutions as their unit of concern. I think this is false. Everytime someone uses a trig identity or takes a derivate, they are using arc-length as their unit of concern. You may not have realized it, but that is what was happening. To speak merely of "rotation" and be disconnected from any kind of length or position in coordinate space doesn't allow you to do anything useful, and you have a degree of freedom in choosing what is a full revolution and now you have to do bookkeeping with coordinate transformations that ugly up all your formulas and and add extra steps. The radian is the natural unit to use: 1 unit of distance of arclength. You are not better off with a fake degree of freedom and then transforming back and forth whenever you need to work with any kind of function relating that angle to a length or rate of change. Moroever when you start generalizing to other curves -- for example, hyperbola and working with hyperbolic sines and cosines, it no longer makes sense to speak of rotations per se as these need not be periodic at all, but it makes a lot of sense to speak of arclength. Arclength works on any curve. It is just distance, it is canonical. It is the natural unit that measures how far you have travelled along a curve (once you select an orientation), thus allowing for a consistent approach and unification of all these identities.