Key Leads and Inertia

[Sarah Fox]

Hi Ric,

Cool applet! :-)  Anyone using it should be aware that the rotating platform
has mass, else the acceleration of the hanging mass (whatever amount of
mass) would be 9.8 m/s^2 with the platform unloaded.  Also, be aware that
the amount of hanging mass is not equivalent to tangential force, but the
two are of course related -- the best approximation occurring when the least
weight is used and the acceleration is the least (i.e. and farthest from the
asymptote of 9.8 m/s^2).  Anyway, yes, the applet applies perfectly to the
touchweight issue.

>From a static, touchweight perspective, 500 g on the outer perimeter is
equivalent to 1000 g mid-way out on the platform (half the radius).
However, from the perspective of dynamic performance, the 1000 g solution
yields a lower moment of inertia (by half, ignoring the unknown moment of
inertia of the supporting platform) and is therefore capable of greater
rotational acceleration with the same tangential force (similar to finger
pressing down on end of key).  (Of course we can't see the full magnitude of
the effect, since the platform has unknown mass.  To minimize the
contribution of the platform, place lots of mass on the platform.)

Thanks for pointing us to this cool virtual demonstration!

Peace,
Sarah

----- Original Message -----
From: "Richard Brekne" <Richard.Brekne@grieg.uib.no>
To: "Pianotech" <pianotech@ptg.org>
Sent: Thursday, May 01, 2003 5:53 PM
Subject: Re: Key Leads and Inertia


> Ok guys..
>
> Now I could admitedly be misunderstanding something here. But I just ran
an
> applet that deals with what looks to be a pretty similiar problem
situation.
> And the results are this
>
> 100 grams force pulling on a horizontal rotation platform where in the
> following weights were pulled around at half way out on the platform and
all
> the way out on the platform
>
> half way  500 grams  acelleration 1.3915 ms^2
>
> all the way out 250 grams acelleration 1.1819 ms^2
>
>
> This all seems like really close to our action situation where point mass
> corresponds to a lead weight, and the platform is our key. Looks to me
that
> more mass closer to the center acellerates faster.
>
> Check it yourself
>
> http://www.explorescience.com/activities/Activity_page.cfm?ActivityID=28
>
>
> Cheers
>
> RicB
>
>
> --
> Richard Brekne
> RPT, N.P.T.F.
> UiB, Bergen, Norway
> mailto:rbrekne@broadpark.no
> http://home.broadpark.no/~rbrekne/ricmain.html
>
>
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