Why is the price of new tonearms so high

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...

Furthermore I was referring to the inertia and you are referring to the effective mass.

Yes, we are indeed talking about the same thing. The "effective mass" of a tonearm is the inertial mass of the end where the cartridge bolts on. The interchangability of inertial mass and gravitational mass is fundamental to classical physics . . . as P=mv and F=ma . . . mass = inertia.

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.

Well, yeah . . . any simple analysis of the tonearm/cartridge resonance envelope shows that in the audioband, if there is vertical modulation, there must be vertical movement of the headshell.

But that's not what we're talking about here . . . . we're talking about the reflexion of VTF as it varies with vertical headshell position, which is why Mark is analysing this in terms of record warps. And here the question is exactly about record imperfections, NOT audio-related vertical modulation.

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.

Yes, angular movement . . . but the force we're talking about is being applied to the end of the tonearm, which is where the effective mass is measured. The angular force vector around the vertical bearing will of course change with all different manner of tonearm-design factors (including effective length) but is irrevelant to the cartridge between two tonearms that have the same effective mass.

Quod erat demonstrandum in realitas mobilis versus modelus in spiritus ?

Oder . . . herrum sitzen und daumen drücken?