Radial spin coordinate mapping problem

Somehow I can’t get a radial grain look on the top of objects because the grain will just stretch along the outside of it.
Here is a cylinder as an example. The sides look as they are supposed to, but the top is flat. It is supposed to look spun in the direction of the grooves of a record. (I’ll use this to enhance an anisotropic shader.)

Could somebody please point out what I’ve got wrong here?