Keyweights and moment of inertia

[Richard Moody]

The encyclopedias have not given a good working definition of "moment of
intertia". 
	What  is of interest to piano technicians seems to be how much force upon
the key is required to produce how much volume of tone. For us, inertia
seems to be how much force is required to accelerate a mass from rest. The
distance the mass travels is limited, but once again here is where I miss
the point of physics.  If the distance is limited why not the acceleration
and velocity? 
	Never the less, strike a piano key.  How much force did you impart? 
Without measuring, all you can tell is by the volume of tone and the
sensation in the finger. 
	I suppose  a device could be made out of a piano key on a balance rail,
that instead of operating a wippen, tosses a ball into the air. Much like
that carnival attraction of the he-man with the sledge hammer ringing the
bell.
	How high the ball goes is  how much force you struck the key with.  A
weight could be dropped on the key and the heights of the ball measured. 
Since the finger never comes down from a height of more than 12 inches our
dropping weight shouldn't either. A crude device you might say in this
marvelous age of precise electronic measuremnts, (so go pay for it) but
how much would say a
10 lb weight have. or a 2 lb weight dropped from say 6 inches? as compared
with your fingers comming down fron the same  height? 
	Primative is it may seem, such a device could provide an insight to
"keyweights and moment of intertia".  The question here is what if any
different force is required to move a key with three weights close  to the
fulcrum as opposed to one weight nearer the end? 
	Also to keep in mind is the reaction of the action assembly to push the
key back up to starting position. It is the down weight of this (minus
friction) that causes the key go back up.  Does the position of the key
weights matter in this? 

Richard Moody 

ps If there are any physics majors on the list, is there a simple answer
to "When does instantanous acceleration equal velocity?"  So why are we
concerned with acceleration instead velocity at the last instance? Are you
saying it doesn't take time for force to develop?  The more time a mass
accelerates the more force it has. But how come this is per sec squared. 
couldn't it be slower than that? 


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