Key Leads and Inertia

[Sarah Fox]

Hi Richard,

The moment of inertia, I, is:

I = mr^2,

where

m = mass
r = radius from axis of rotation

I is additive, so if there are two masses, it's the sum.  If you have a
solid object, rather than point masses, you just have to calculate the
integral.  For a key stick (assuming it is a uniform stick, which it is
not), the following might come close:

I = [ m (f^3 + b^3) ] / [ 3 ( f + b) ],

where

f = the length from the fulcrum to the front of the stick, and
b= the length from the fulcrum to the back of the stick
m = mass of the entire unweighted stick, with capstan removed.

You can add in inertia from lead weights and the capstan, however
appropriate.

In reality, it's a lot more complicated.  The stick is not uniformly shaped
and has stuff stuck on it like buttons, and keytops.  The general equation
for a uniform stick rotating about its end (used to derive the above) would
be:

I = 1/12 mL^2,

where L = the length of the stick.

Anyway, it depends on the keystick.  You'll have to measure, weigh, and
calculate for yourself.

Peace,
Sarah


----- Original Message -----
From: "Richard Moody" <remoody@midstatesd.net>
To: "Pianotech" <pianotech@ptg.org>
Sent: Thursday, May 01, 2003 10:09 PM
Subject: Re: Key Leads and Inertia


> What is the formula? for inertia?
>
> ----- Original Message -----
> From: Don <pianotuna@accesscomm.ca>
> To: Pianotech <pianotech@ptg.org>
> Sent: Thursday, May 01, 2003 12:33 AM
> Subject: Re: Key Leads and Inertia
>
>
> > Hi Richard,
> >
> > The inertia goes up by the *square* of the distance from the
> fulcrum--so
> > yes three weights would likely have less inertia than *one*
> farther from it.
> >
> > Run the numbers
> >
> > 30 grams x 1 cm from fulcrum = 30
> >
> > 10 grams x 3 cm from fulcrum = 90
> >
> > If I'm wrong please let me know *grin*.
> >
> > Regards,
> > Don Rose, B.Mus., A.M.U.S., A.MUS., R.P.T.
> >
> > mailto:pianotuna@accesscomm.ca
> > http://us.geocities.com/drpt1948/
> >
> > 3004 Grant Rd.
> > REGINA, SK
> > S4S 5G7
> > 306-352-3620 or 1-888-29t-uner
> > _______________________________________________
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> https://www.moypiano.com/resources/#archives
>
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