Home Vinyl Asylum

Welcome Licorice Pizza (LP) lovers! Setup guides and Vinyl FAQ.

[ Follow Ups ] Thread: [ Display  All  Email ] [ Vinyl Asylum ]
[ Alert Moderator ]

OK , here goes.

So that we don't have to continually solve integrals we'll use an algebraic conversion. For a body with uniform weight distribution per unit length and negligible width in proportion to its length, we can write dM = M/l dx

So ∫x 2 dM becomes ∫x 2 M/l dx. This solves to M.l 2 /12. This is the moment of inertia around the centre of mass, I cm .

The moment of inertia for any body around any point is I cm + M.x 2 where x is the displacement between the centre of mass of the body and the pivot in question.

Thus for the first example given
Headshell 7g x (40 2 /12 + 220 2 ) = 339733
Armtube 15g x (180 2 /12 + 110 2 ) = 222000
Bearing 60g x 40 2 /12 = 8000
Counterweight 150g x 21.27 2 = 67862

Total = 637594, divided by 225 2 gives 637594/50625 = 12.5.

The approximation is probably not really valid for the pivot structure which does have significant width in porportion to length but it is such a small part of the sum it doesn't really matter. Similarly considering the counterweight as a point mass is an approximation but it also has little effect unless the counterweight is very close to the pivot.

Mark Kelly

This post is made possible by the generous support of people like you and our sponsors:
  Kimber Kable  

Follow Ups Full Thread
Follow Ups
You can not post to an archived thread.

[ Top Top of Page ] [ Contact Us ] [ Support/Wish List ] [ Copyright © 2025, Audio Asylum, all rights reserved ]
[ General ] [ Speakers ] [ Tubes ] [ Vinyl ] [ Digital ] [ Hi-Rez ] [ Video Asylum ] [ Cables ] [ Tweaks/DIY ] [ Music ] [ Films ]