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Effective mass, moment of inertia and counterweights.

Posted by Mark Kelly (M) on November 17, 2005 at 01:18:50

Here I go again, but I have to make sure I am straight on all these things.

As I understand it, "effective mass" for a tonearm is the moment of inertia I _cm divided by the square of the stylus to pivot distance. Thus a standard 225mm tonearm with an effective mass of say 10 grams has an I _cm of 5.06 x 10 ^-4 kgm ² .

The I _cm is the sum of all the masses of the parts of the tonearm multiplied by the square of their distance from the pivot and this includes the counterweight.

By this logic using a counterweight made from a very high density material (like tungsten), which can be mounted closer to the pivot for a given balance point, reduces the counterweight's contribution to the I _cm of the arm. As I see it, this is a benefit when designing an arm to reach a certain effective mass target because it allows the designer to use more mass where it is needed, between the arm and the pivot (on the grounds that increased mass here allows one to increase stiffness or add damping materials or whatever else one desires).

BUT, on an already existing arm it doesn't have the same effect. Given the relationship between I _cm and effective mass anything which reduces one reduces the other, so the major effect of such substitutions would be to change the effective mass. I always thought there was an optimal effective arm mass for a given cartridge which put it right in the middle of the range of resonant frequencies. Yet the proponents of using substiute weights imply that this is not so, and reducing I _cm and thus effective mass is always a good thing.

Are their arguments based on something I've missed, or are they marketing hype?

Mark Kelly

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