Hey! I was reading Goldestein's book on classical mechanics and I came across this (Page 20 3rd Edition): "Note that in a system of Cartesian coordinates the partial derivative of T with respect to qj vanishes. Thus, speaking in the language of differential geometry, this term arises from the curvature of the coordinates qj. In polar coordinates, e.g., it is in the partial derivative of T with respect to an angle coordinate that the centripetal acceleration teml appears." Here T=Kinetic energy of the system qj= the jth generalized coordinate. I don't exactly understand how this works. 1.Why isn't it (dT/dq) zero in polar coordinates if it is zero in cartesian coordinates? 2.What if velocity was a function of coordinates? dT/dq can't possibly be zero even in cartesian coordinates then right? I might have missed some assumption that makes everything clear, so all those of you who've read the book, please help!