Tonearm effective mass

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.
Raul.

Raul

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.
Raul.

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.

Hdm,
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.
Raul.