Tonearm effective mass

If you add more weight to the counterweight on a tonearm does the tonearm effective mass go up or down?

Dear Badcap: Go up but the change in the effective mass will be small due that the counterweight is near the tonearm pivot.

If you need a significant change in the tonearm effective mass and if you can then you have to do it at the tonearm headshell position.

Regards and enjoy the music.
Correction. If ALL you change is the counterweight (same cartridge, same mounting screws, etc.):
- a heavier c/w closer to the pivot REDUCES effective mass
- a lighter c/w farther from the pivot INCREASES effective mass

Effective mass is a function of mass X the SQUARE of the distance from the pivot, so changing the distance has a larger effect than a change in mass.

Aside from that, for practical purposes I agree with the rest of Raul's post.
Thanks I thought I had read a heavier counterweight with everthing else the same would lower the effective mass. So it would take a big increase in weight to make very much of a difference? I am trying to get the resonant frequency up to 10 from 8 with a fixed headshell.

Doug: Thanks for that information. It is both counterintuitive and very relavant to me at this time as I am in the process of doing a tonearm upgrade and one of the goals is to increase effective mass of the tonearm (cartridge is a wood bodied Denon 103R). I am looking at changing out the stock headshell on the new tonearm (stock headshell weighs about 6-7 grams) with an aftermarket headshell that weighs 16 grams.

I've been assured by someone who owns the same tonearm that the stock counterweight on the arm will balance out the cartridge and heavier headshell. There is also an optional heavier counterweight available for the arm to balance out heavier cartridges. I'm assuming, though, from what you say, that the lighter (stock) counterweight in this situation is going to result in higher effective mass.

Would you concur with that? Thanks in advance.
Dear Doug: The question speaks to add weight to the counterweight, IMHO if you add weight at any position of the counterweight the effective mass goes up against the original one ( obviously with out change in the original counterweight position. ).
A plain answer to a plain question.

Regards and enjoy the music.


Doug is completely correct as long as the dimensions of the counterweight do not change*.

Remember that "effective mass" is actually the moment of inertia of the arm divided by the square of the pivot to stylus distance. Doubling the conterweight mass and moving it half the distance to the pivot halves its contribution to the moment of inertia because 2 x 1/2 x 1/2 = 1/2.

The counterweight is usually responsible for between 20 and 40% of the moment of inertia of an arm, therefore doubling its mass will reduce the moment of inertia by around 10 to 20%.

* If you make the counterweight larger a second effect comes into play: the moment of inertia of the counterweight about its own centre of mass will increase and this will affect the arm as a whole according to the parallel axis theorem. You could double the mass with the same dimensions by making the counterweight from a material with twice the density of the original - changing from brass to a tungsten pseudo alloy would be very close to this.

Dear Quidity: I'm just saying that the thread question was a plain one ( almost a yes/no. ) where you can choose to answer in the same plain way ( like me ) or in more wide way like Doug, that's all, please read the question again.

I know perfectly how " works " the effective mass subject. I'm not in disagreement with you or Doug.

Regards and enjoy the music.
Excellent clarification by Quiddity, thanks. I should have included the proviso that the two c/w's be of the same shape.

With apologies to my friend Raul, this question is not as simple as you say. You're correct that changing to a heavier c/w would increase effective mass (moment of inertia) IF you mounted the heavier c/w the SAME distance from the pivot. But that would unbalance the cartridge, so this fact has no real world application.

For the *same* VTF...
with the *same* cartridge...
for two c/w's of the *same* shape but *different* masses...
the heavier c/w mounted closer to the pivot will result in a lower moment of inertia than the lighter c/w mounted farther from the pivot.

You left out a key factor. The heavier headshell will be mounted at (virtually) the same distance from the pivot as the lighter headshell. Therefore, its greater mass will increase the system moment of inertia, quite substantially given how much heavier it is.

Read Quiddity's excellent post. A headshell is mounted farther from the pivot than a c/w, so a change in mass at the headshell has a greater effect on moment of inertia than does the corresponding adjustment of c/w position. Adding mass at the headshell and adjusting the c/w to maintain the same downforce at the stylus increases moment of inertia (as Raul correctly stated above).

This will be true whether you use the existing c/w or go to a heavier one, although in the latter case the increase in moment of inertia will be less, due to the effect that was the original topic of this thread.
Doug: Yes you are right: my answer was to much plain. But what I was trying to say was that to really make a difference in the effective mass and due that the headshell is at the " farest " position from the tonearm pivot then here at the headshell is a good place to do it, that's all.

Many times I think the things and the explanation only I understand it like a whole, like in this time. I will try to be more precise.

regards and enjoy the music.
Thanks again Doug (and Quiddity). I understand (now) that it's a given that the heavier headshell will have a much greater effect on increasing mass than messing with counterweights.

It was interesting to me that a lighter counterweight pushed out further from the pivot might have as much (or greater) effect in increasing or maintaining a given effective mass than a heavier counterweight balancing the same cartridge closer to the pivot point.

Following this, my next question is this: given that a lighter counterweight is capable of balancing out the same cartridge (but obviously further back from the pivot) that a more substantial counterweight can, would there be any sonic advantage to using the heavier countweight mounted closer to the pivot assuming the effective mass is approximately the same? Would there be a sonic advantage or improvement using the heavier counterweight closer to the pivot point?

Does anyone have any experience with this or any ideas as to whether one approach would be better from a sound perspective than the other?

I agree that for practical purposes moment of inertia changes must be made at the headshell end. (Of course as you know, raising headshell mass can impair tracking performance over warps, there's no free lunch.)


The answer to your last question will be specific to the tonearm and cartridge. The difference in moment of inertia caused by changing counterweights (very small difference, as Raul points out) is unlikely to make as much sonic difference as the change in the system's INTERNAL resonance behavior.

I'm not talking about the change in resonance frequency of the spring-loaded cartridge/tonearm system that we've all seen the math for, and can demonstrate with the HFN record. Moment of inertia is of little sonic significance unless you make a BIG change. I'm talking about how the cart/arm reacts to stray energies in the audio band being fed from the cartridge into the tonearm. That will vary depending on the equipment.

The only way to know is to try, unless someone has tried the same combos before and can report.