Lewm,
If there was no groove, the arm would skate and rotate until there were no forces acting to make it do so, so there would be, for a short while, a "conventional" centripetal force acting on the stylus and arm along the stylus to pivot axis caused by the rotation.
When there is a groove, the inside face restrains the stylus, so there is effectively no such force, because the arm is rotating only minimally (at less than 0.01 rpm), and the stylus has such a tiny mass, that any forces are negligible, and totally overwhelmed by the friction forces by many orders of magnitude.
J
If there was no groove, the arm would skate and rotate until there were no forces acting to make it do so, so there would be, for a short while, a "conventional" centripetal force acting on the stylus and arm along the stylus to pivot axis caused by the rotation.
When there is a groove, the inside face restrains the stylus, so there is effectively no such force, because the arm is rotating only minimally (at less than 0.01 rpm), and the stylus has such a tiny mass, that any forces are negligible, and totally overwhelmed by the friction forces by many orders of magnitude.
J