Why does anti-skate on record players work the way it works?

Question

Upon researching record players, and especially setup and maintenance of these, I have found information about the "anti-skate" feature of tone arms.

Every online resource I found said that anti-skate applies an outwards force on the stylus to counteract its tendency to move inwards, to reduce wear on the inner groove wall, but without providing any additional information.

This is extremely counter-intuitive: from my understanding, it is the record that pushes the stylus inwards, or more precisely, the outer groove wall pushes the stylus inwards, towards the inner groove wall and towards the record center. The only force pushing the stylus against the inner groove wall is gravity, because of the groove's V-shape.

Why would the stylus naturally push stronger against the inner wall rather than the outer wall? Why should we apply an outwards force on it, when Newton's First Law is already doing so? And in general, what is the point of anti-skate?

Answer 1

The most concise explanation of the physics I was able to find was a diagram (https://www.audioasylum.com/cgi/vt.mpl?f=vinyl&m=1183498) by John Elison in the Vinyl Asylum forum, and a modified version on page 3 of the summary article "Skating force - Misunderstanding and misinformation about it.", by Hakan Agustos (https://www.audioasylum.com/images/Skating-force-Misunderstanding-and-misinformation-about-it.pdf).

The frictional force at the stylus acts tangentially to the record groove*, but the tangent line does not pass through the tonearm's pivot point, where the reaction force is applied, so the frictional force can be resolved into two components, one pointing directly away from the pivot point, and another perpendicular to it, which although it does not point directly towards the spindle, does point more towards the center of the record than the outside.

In the absence of an anti-skate mechanism placing a torque on the arm to provide a countering outward force, the inner groove wall must provide it.

* Opposite the direction of motion of the stylus relative to the groove.