What's all this I hear about Inertia ?

[Don Mannino]

David,

Sometimes when we try to simplify things too much, we find out that we
forgot some things.

One problem that you did not consider, I think, is that inertia when a mass
is rotating is calculated quite differently than when that same mass is
simply set in motion in a straight line.

I like to use the playground teeter-totter as an example.  You can balance
it by placing identical amounts of mass on either end.  It doesn't matter
how much mass you put there, it will always be in balance - the downweight
(if there were no friction) would be zero.

But two masses of one kilogram would be much easier to get moving than two
masses of 100 kg. The more massive balance would be much harder to get
moving.

Also, if you move those two masses equally towards the pivot point, so that
they were very close to the pivot, then felt the resistance to movement at
the ends of the lever, you would find it much easier to move again - as if
the mass had been removed.  This illustrates that the leverage affects the
inertia, even though the mass has not changed.

Don Mannino

-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of David B. Stang
Sent: Monday, September 29, 2008 11:48 AM
To: pianotech at ptg.org
Subject: What's all this I hear about Inertia ?

There seems to be a lot of confusing talk in the piano tech world
about "key inertia". I was confused, too, until I went back to my
physics textbook and found:
Inertia by definition means resistance to acceleration, and (at
speeds lower than the speed of light or so) inertia and mass
are identical.  And weight is proportional to mass on the surface
of a particular planet.

In summary:

Two items of the same weight have the same inertia here on
Earth. Period.

If a perfectly rigid key weighed 1000 pounds overall but were
balanced to have a certain down-weight, it would behave and feel
the same as any other rigid key with the same down-weight.

But we all know that a key with less weight in front has more
dynamic range.
The key, pardon the pun, is the rigidity.
When I press a key I am wasting energy for a very small amount of
time when I am overcoming the weight (i.e. inertia) in the front of
the key because it bends. There would be less wasteful bending and
more dynamic range if there were less weight in front. Correct me if
I'm wrong here, but I think the concept is as simple as that.  No need
to fabricate a giant experimental contraption and write a multi-part
journal article about it.

Another aspect of this is time: the weight can change over the
duration of the key press. This is why damper regulation can be
important. But, again, a simple concept.

I think a lot of us are confused about this stuff when we don't really
need to be.  The hard part is figuring out how to engineer a key
to behave at its best.