Tonearm effective mass

Here ya go!

http://www.mh-audio.nl/Calculators/RF.html

Moment of inertia Is seldom used to determine cartridge compliance mostly due the complexity of this calculation. The manufacturer might have done this during design but not very practical for field cartridges installation.   

Adding weight lowers the resonate frequency. 

P.S. It's not really rocket science because you basically have high compliance or low compliance cartridges. A quick call to the tonearm manufacturer will help with cartridge selection as will seeing what cartridges the factory can supply with their product.  

@yogiboy 

trying to understand this a little better with my Acoustic Signature 12”

TA-1000 tonearm. Maybe I’m not seeing the right specs for the two cartridges I’d like to pair, Umami Red and AT-ART9xa. 

The AT-ART 9xa shows a weight of 8.5 grams and compliance of 20x10-6 at 100hz. The Umani Red does not give a compliance spec. BTW, Japanese cartridges compliance figures are not at 10hz they are at 100hz so you will have to multiply by 1.7 to get the correct resonance frequency calculation figure. With your 12 gram tonearm and that ART, the resonance frequency is 6hz!

6 hz is very good! Resonance frequency should be below 10 hz!

This article explains arm and cartridge compatibility!

@jw944ts , that is exactly how you tune the arm, by adjusting the mass at the cartridge end. Soundsmith has a very nice set of graded cartridge screws. If the resonance frequency is too high you add mass until you get it down to between 8 and 12 Hz. If too high you have to subtract mass. It is easy to add mass to a light tonearm but very difficult to subtract mass from a heavy one. You need a test record with resonance tracks to do this. Trying to calculate the required effective mass is almost meaningless as specs can be off enough to invalidate the math. It is always best to test the arm and find out exactly what it is doing.

The calculation charts are very useful at getting a ballpark figure before you purchase a cartridge. A test record is great ( I have one ) but you would be using it after you made the purchase. If you have to remove mass then you will be SOOL!!

Dear @jw944ts  : "  ie heavier screws, in attaching the cartridge to the headshell...would this not, as well, increase the effective mass/moment of inertia?  "

The plain answer is yes but you do not be anal to this issue .

Regards and enjoy the MUSIC NOT DISTORTIONS,

R.

+1, Raul.

In the calculation for effective mass, all mass counts, including the weight of the cartridge itself, the weight of the headshell, and the weight of any hardware.  Thus using heavier than normal screws will increase the calculated effective mass, M.  Because the screws are essentially in the same physical location as the cartridge, and because that net mass is at the very end of the tonearm, adding heavier screws has a more or less linear effect on the effective mass, M.  In other words, if the new screws weigh 2g more than the old ones, add 2g to effective mass. Since resonant frequency is in the denominator of the equation used to calculate it, any increase in M will lower Fr.