MC, Yes, if you can draw a straight line from stylus tip, through the cantilever, that intersects the pivot point, then you have zero skating force. And to Larry, yes the reason conventional pivoted tonearms that are mounted so the stylus overhangs the pivot and which incorporate an offset headshell NEVER exhibit zero skating force is because, even at either of the two null points (where the cantilever IS tangent to the groove walls), the offset headshell alone creates a skating force. But no, MC, not every pivoted tonearm exhibits a skating force at all times. Underhung tonearms, of which there are only a few, that have zero headshell offset, will give only one null point on the surface of an LP, but at that one null point, the skating force is momentarily absent, because the tonearm meets the criterion stated in my first sentence. (Pivoted tonearms that incorporate complicated mechanisms for maintaining tangency to the groove at all times are not part of this discussion.)
Mijo, "mu", the coefficient of friction is non-negotiable and is not dependent in any way upon surface area. Testpilot got it right. It is a constant for any two materials. There are tables showing coefficient of friction for a wide variety of material pairs. Someone else mentioned velocity. No, friction force is not dependent upon velocity, either. Also, can you say where you got the idea that a stylus tip gouges a grooveless LP? Before you go quoting the "tremendous" pressure of a stylus tip on vinyl, which is arrived at by extrapolating the teeny-tiny surface area of a stylus tip to a square inch and multiplying the VTF accordingly, I doubt the validity of making that extrapolation. But I am open to contrary evidence that I might be wrong.
In my opinion, the reason that running the stylus on a grooveless LP does not mimic the skating force generated while playing music is that in the process of negotiating the tortuous groove, the stylus tip is constantly subjected to acceleration and deceleration (acceleration = change in stylus velocity, as someone else mentioned; deceleration = negative acceleration). Each tiny acceleration requires a Force (F = ma), because the stylus tip has mass, pulling the stylus in the same direction as that of friction. That force is adding to the friction force in a way that does not happen when there are no grooves and no music.