MC's thoughts are a minor consideration in thinking about the magnitude of the skating force. The most important cause of the skating force (after friction) is the tracking angle error, which is varying in terms of degrees of angle, all across the surface of an LP. And it is never zero, for any of our conventional pivoted tonearms that have an offset headshell, even at the two null points you can achieve if you align the tonearm according to any of the known algorithms.
The movement of the stylus in the groove generates a friction force. If the vector direction of that force were to be straight back along the cantilever, and if the cantilever were to align with the arm wand going all the way back to the pivot, there would be no skating force, regardless of the tortuosity of the grooves or the ups and downs of the music signal. But that never happens with our pivoted tonearms; there is always an angle of error. That generates the side force. If you want more on this subject, I will try to help, but otherwise, I don't want to put anyone to sleep. Think of the little red wagon you had when you were a kid. It had four wheels and a pull handle that was attached to the axle of the front pair of wheels. Remember what it was like to try to keep the wagon alongside of you while you dragged it down the street? There was an aberrant side force that you had to correct for. That's the same idea as skating force.