Why is the price of new tonearms so high

Assume a standard "taco warp" so the warp frequency is 7 rad.s^-1.

Hi Mark - please, what's a "taco warp"? I'm assuming it's not related to female tonearm connectors :) . . . but seriously, while I can't really conceive of a standard shape to the minor warps on my records (for those that actually get played, not the obviously 'defective' sort) . . . just going by the tempo of the excursions, I'm guessing that 1-3 Hz is about the frequency range of most of them. So your 7 rad/sec (a little over 1 Hz) is a good figure, but probably a little far away from resonance for calculating good maximum/minimum changes in VTF.

If the inertial mass were 25 g (say 15g arm plus 10g cartridge) and the warp were 5mm high, the maximal variation would be around 6.2 mN. A similar calculation allows a maximal warp tolerance to be derived for any arm / cart combination as a function of VTF.

But the record doesn't act directly on the effective mass of the arm/cartridge - the compliance of the cartridge is in series. So for the actual change in VTF, you'd need to add a scaling factor based on the cartridge/arm resonance, no? Also, the point of maximum/minimum force in the warp cycle will change with warp frequency, as will the phase relationship between the force exerted by the record on the stylus and the force exerted by the cartridge on the tonearm will change as the warp frequency approaches the primary resonant frequency.

Which makes me think that in most cases, the minimum/maximum cases of effective stylus VTF are unlikely to occur very near the tops/bottoms of the warp excursion, meaning that we're also going to see these extremes as occuring at a slightly altered VTA, the extent of which depends on the slope of the warp, hence its amplitude and frequency. Now my head's starting to spin . . .

The important point is that it has nothing to do with the balance of the arm but is stictly related to the moment of inertia (and the mass of the cart).

Yes, this is indeed the important point . . . but I would clarify that it's the moment of inertia from the effective mass of the arm/cartridge combination, coupled with the resonant behavior of the cartridge compliance interacting with this effective mass.

But the big point with static vs. dynamic-balance is . . . what exactly is issue that the dynamic-balance system is trying to solve? Is it always used as an attempt to improve the constancy of VTA with tonearm position? In the tonearms I've set up, it seems that many are position-sensitive (remove the mat from under the force gauge and get a different reading, etc.), and many are not . . . and this doesn't necessarily correlate with whether or not the particular tonearm has a dynamic-balance system. So it seems to me that it's more in the overall execution than anything else.

Just a short note from the office between two meetings....

I don't think I was completely wrong.
The inertia in a tonearm/cartridge combination does depend on the effective length, as this is not a homogenous corpus, but the majority of the mass is situated at the very end of the moving corpus - thus the inertia in a say 15 grams effective mass 12" tonearm with a given cartridge is always larger then in a 15 grams 9" tonearm with the very same cartridge.
Inertia is increasing with the distance to the center of movement.
The more so, the further away the majority of the mass from the dead center of movement.
Now we get closer to the model of a tonearm w/cartridge mounted far away from the pivot.
With the model of a pivot tonearm we are looking at the simplified calculation (taking the tonearm as a mass homogenous corpus) of (following Steiner AND WITHOUT including the cartridge mass at the moving tip of the lever !): J = 1/3 m x (2R) sq

J = inertia
m = mass
R = radius
sq = square

More to follow tonight.

thus the inertia in a say 15 grams effective mass 12" tonearm with a given cartridge is always larger then in a 15 grams 9" tonearm with the very same cartridge.

No. This is the classic "which is heavier, a pound of lead or a pound of feathers?" axiom. It's just that 12" tonearms tend to have higher effective masses than their 9" counterparts of the same make and "model", because they're bigger.

Inertia is increasing with the distance to the center of movement.

This would be true if we were assuming a constant angular acceleration about the vertical tonearm pivot, but we're not. We're assuming a constant linear (okay, circumferential) acceleration at the end of the tonearm.

Again . . . if the moment of inertia, applied (circumferentially about the tonearms' pivots) to the end of two different tonearms is different . . . then their effective mass is NOT the same. QED.

Dear Kirkus,

*****thus the inertia in a say 15 grams effective mass 12" tonearm with a given cartridge is always larger then in a 15 grams 9" tonearm with the very same cartridge.

No. This is the classic "which is heavier, a pound of lead or a pound of feathers?" axiom. It's just that 12" tonearms tend to have higher effective masses than their 9" counterparts of the same make and "model", because they're bigger. *****

well.... I am kind of familiar with the feather/lead picture which I used (guess like many fathers..) to illustrate the point of gravity to my son once.
Furthermore I was referring to the inertia and you are referring to the effective mass.
Common knowledge assumes, that we do not see a vertical movement in the tonearm, but we do - and do so constantly during play.
I believe (think, know, have had it checked at the technical university Munich in 1995 with precise laser graphics - choose one), - and this is backed by technical papers of the record industry too - that there is a (although tiny in distance) constant vertical movement while playing a record.
The surface of a vinyl record is anything but dead mirror flat.
It does consists of hundreds hills and valleys (not warps) due to fluctuations in thickness as result of the molding process.
These are minor, but so is the contact area of the stylus.
So I think we do see a vertical angular movement - not constant, but even worse alternating in direction - even if not always apparent to the eye.
Based on this model my assumptions aren't that far fetched anymore.
Quod erat demonstrandum in realitas mobilis versus modelus in spiritus ?
Yet ?

Kirkus,
I don't get your last comment (unless Mark's comment that effective mass = moment of inertia divided by square of effective length is wrong). If Mark's equation is right, the two could be different and still result in an identical third (effective mass) value.

Mark,
The reason I asked my question above was that I thought, as Kirkus later suggested, that the compliance is in series with the moment of inertia on any change in aspect of the record (which we know has a VTF delta, but also has a VTA delta). I have forgotten much of my physics (and probably never knew as much as you have forgotten, even though it seems you haven't forgotten anything) but I would have thought the compliance was a significant 'external force' with regard to the d"Alembert principle.

In any case, leaving aside compliance effects, I would have thought that for a given mass of cartridge at the end of a given tonearm length, a spring-loaded system would reduce the effective length of a tonearm vs a gravity-loaded system. Would this not mean, assuming identical mass and tonearm length, that a spring-loaded system had a lower moment of inertia? Hmmm... Am I taking the number out of one side and not both?

I should go read a textbook again...