Inertia

[James Ellis]

In one of my first posts on this subject, I used an unfortunate choice of
words, and that set off a series of misunderstandings.  My apology.  So
that you don't think I have lost my mind, I'll try to clear this up.

During that flurry of comments, someone (don't remember who, doesn't
matter) misquoted Don as saying that inertia was not related to mass.  I
went back and read Don's posts, and he did NOT say that.  Inertia is
directly related to mass.  A lead ball the size of a ping-pong ball
certainly has a lot more inertia than the ping-pong ball because it has a
lot more mass.

Someone else said that mass and weight were directly related.  That's true
only at one given location on the earth.  Otherwise, it's not ture.  Weight
is simply the force of gravity on a given mass.  It would be very different
on the moon, or Mars, or Jupiter.  We should not say "weight" when we mean
"mass".  However, when we say "Touch-Weight", we are talking about a static
condition, and we are simply specifying the weight required to barely move
the key, or to balance it, etc.

Inertia is the force required to accelerate or decelerate a mass.  There
are a varitey of ways we can say this.  A fly-wheel has the same inertia
whether it is spinning or stationary.  However, if we have a stick that we
are going to hold by the end, and swing back and forth, and we have a mass
that we can clamp at any location out on the stick, then the "moment of
inertia" of that mass (just the mass, not the stick) will be proportional
to the square of the distance between our hands and the mass.  I.e., if we
swing the stick through a given angle, the force required to accelerate and
decelerate the mass will be proportional to the square of its distance from
the hands.  The reason for this is because the kinetic energy stored by,
and given up by, the mass as we accelerate and decelerate it, is
proportional to whatever the V sq of the mass turns out to be as we swing
it back and forth.  Now, think of that "stick" as a hammer shank, or a key.

Kinetic energy is dependent upon inertia and motion.  If there were no
inertia, there could be no kinetic energy.  If motion is zero, kinetic
energy is zero.  Kinetic energy is stored by the inertia of the mass in
motion, and it is proportional to the square of the velocity of the mass.

Translating all this to the piano action, in my previous post, I showed why
a lead weight in a key has far less effect on the "moment of inertia" of
the action than does the hammer head.

Jim Ellis