In summary,
A. The stylus on a traditional turntable wants to "skate" towards the center of the record.
B. How hard it wants to skate is proportional to how far it is from the center of the record.
C. If you don't counteract this force the stylus tip will higher on the inside of the groove than on the outside.
D. This will result in:
D1. An imbalance between the audio response between the two channels.
D2. Increased wear on the inside of the groove wall.
E. You counteract the skating force with anti-skate (spring, weight, electronic mechanism, etc.) which, ideally, varies in proportion to how far the stylus is from the center of the record.
ALL ANTI-SKATING MECHANISMS ACHIEVE THEIR INTENDED PURPOSE BUT ARE NOT PERFECT!
... then again ... they don't call this the disinformation superhighway for nothin'
Caveat: I'm an engineer and can accept "close enough" - if you are physicist well .....
Manfred/lini - chime in when I get it wrong.
I could just wave my hands here and say "Believe!" but ....
Adjusting anti-skate:
Most traditional (modern/vintage) turntables are equipped with a device that will, in parallel with a tracking force adjustment device, prevent the stylus tip from skating across a record. You adjust the this so-called anti-skate device in concert/parallel with your tracking force adjustment to achieve this objective. The people at Technics/JVC/Pioneer/Sony/etc./etc. were pretty intelligent and figured this stuff out for us. I'm assuming that, in the olden days (antiques), you just pushed down really hard on the stylus to keep it from skating but that wasn't very kind to records nor was it very high fidelity.
So, just adjust as the instructions indicate and you should be good to go. If it's a spring based system on a vintage table you might run into a "worn" anti-skate spring (30, 40, 50, 60 years sitting there tensioned and it may lose some of it's "springyness".
In a more perfect world you could ignore the instructions and use a 1 kHz stereo test record and adjust your anti-skate at the outermost and innermost grooves to get proper balance between the channels or, actually, somewhere closer to the outermost groove since that's where the halfway point of the groove (lengthwise) exists.
What was the OP thinking?
Not sure what the OP got right. This business of centripedal force, maybe right in some frame of reference but, WRT to the stylus tip and the record surface not sure where it was going.
At least it made me think through the whole process rather than assuming that the manufacturers got it right.
The gory details!
Apologies to those who fully understand this but just thinking it through.
(Note: if I was a better electronic artist I'd provide drawings but I suck) so you will have to visualize.
The objective is to balance the skating force with anti-skate so the forces acting on the stylus tip (between the left and right groove of the record) are balanced and you get balance between the L/R channel audio and wear.
Why does the stylus want to move to the center of the record (skate)?
Well, for it to want to move there has to be a force acting on it.
If we look at the forces acting on the stylus tip there should be:
(1) The force (weight) applied by whatever "tracking force" is being applied - vertical tracking force (VTF)
(2) The force due to friction as the tip drags across the vinyl grooves - I'll make this up - "tangential (with respect to the record groove) tracking force" or TTF
There are also acceleration forces as the stylus tip follows the deviations in the groove wall (music) but, for the purposes of anti-skate, I only consider their effects on the tangential tracking force as the increase apparent friction between the stylus tip and the record surface.
The TTF is the result of the vertical tracking force (VTF) and the dynamic coefficient of friction between the stylus tip and the vinyl (mu): TTF = VTF x mu. TTF acts "along" or tangential to the record groove.
All of these forces can be variable. The VTF will change if the record that isn't perfectly flat. The TTF will increase as you increase VTF or increase friction (loud low frequency passages). Conversely, TTF will decrease as you decrease VTF or decrease friction (quiet passage or between songs on lp).
Think sliding a box across a surface, as you increase the weight (eg. VTF) or the surface gets rougher (increase mu) the force required to slide the box (TTF) increases proportionally. (won't get into static and dynamic - we're dynamic). Guess you could consider a box that is already sliding and add weight to it - it will slow down. Or, better yet, press harder on your car brake pedal and F1 increases and increases the rate at which you slow down.
I'm getting there.
Now, change perspective from the sylus tip to the tonearm pivot. The stylus is connected to the cartridge which is connected to the tonearm which rests on that pivot.
If you consider a traditional turntable and draw a line tangent to the record groove at the beginning of a record (lp) you will see that it doesn't intersect with the tonearm pivot but passes "outside" the pivot by some distance "R". Since TTF is acting along this line and it doesn't intersect with the pivot you end up with a force acting on an imaginary arm of length R which will push the stylus inwards towards the center of the record
Fskating = TTF * R
Been a long time - think it's Newton's third law. For every action/force there is an equal but opposite action/force or the system will accelerate.
Unless there is something else keeping the tonearm from pivoting the only thing stopping it is the inner groove wall "pushing" on the stylus tip - this is bad.
As the stylus moves towards the center of the record the offset (R) between the tangent line to the groove and the pivot of the tonearm gets smaller.
As a result, the skating force (Fskating=TTF * R) also gets smaller.
Side note: the stylus won't skate if you put enough VTF on it but it won't work sound good and it will increase wear on your record. A U.S. penny is about 2.5 grams. You want a little VTF as possible (as the cartridge/stylus designer wanted) but as you reduce VTF you increase the likelyhood that the stylus tip won't follow the groove and physically skate across the record towards the center.
If we go back a bit, we had defined TTF as being a function of VTF and the dynamic coefficient of friction (mu).
Fskating = TTF * R = VTF * mu * R
If you increase VTF then the Fskating will also increase.
To keep the force on the stylus balanced (between left and right sides of the groove) we need to apply the anti-skate (Fantiskate).
The anti-skating force will need to vary in direct proportion to the skating force, Fs, (larger at the beginning of the record and progressively smaller as the stylus moves towards the center).
Since it's most common, consider an anti-skating spring.
The force applied by a spring, Fspring, is a function of its "stiffness" K and how far from its relaxed position it is, X, so Fspring = K * X.
I don't have one open now and haven't really looked at it but I believe the spring in a common Technics turntable is a leaf spring (flat metal piece) where X is actually the spring deflection from its relaxed position.
If you have another arm connected to the tonearm pivot down below the turntable and put this spring against it will counteract the skating force based on how much it is deflected.
If set up correctly the spring would be fully relaxed when the stylus was at the center of the record and apply increasing force as you move away from the center.
In reality, you turn the anti-skate dial to a setting that the manufacturer determined based on the tracking force and hope that you get balance that is our final objective.
Fskating = Fantiskating
or
VTF * mu * R = Kspring * X (dial setting).
You could also have Fantiskating = m * g * R where m is the mass of a little hanging doo-dad attached to a separate anti-skate arm at the pivot where R is the distance from the pivot center to the attachment point (g is gravity).
Of course, you could also get a linear tracking turntable but what would be the fun of that?
Or, you could have my JVC QL-Y5F where it senses tonearm position and uses electromagnets attached to the tonearm to counteract skating forces and a separate set of sensors/electromagnets to adjust VTF "on the fly" - think warped record. Talk about a nightmare when it fails eh?
Hopefully I didn't make too many errors here. At least I sorta-kinda understand this all now I think.