Inertia

[Richard Brekne]

> Alan McCoy wrote:
> 
> This has been an interesting thread.
> 
> On the one hand we have Don Gilmore who says the following: "Inertia
> is not an inherrent, quantifiable property of an object, it's an
> effect, like the Doppler effect.  There are no units of "inertia"; one
> object cannot have more "inertia" than another.  It can have more
> kinetic energy, or momentum, or mass, or velocity, or indeed "moment"
> of inertia than another object since those are measurable,
> quantifiable properties."
> 
> Then we have Jim E. who states:
> 
> "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."
> 
> We are talking right past each other. I'm with Ric. We need some
> clarity. Oh what the hell, I'll try.

Well, I'm glad you saw that point... actually.. both of them... clarity,
and talking past each other. But to tell you the truth.... I think Don
is wrong, all due respect I am sure... the fact that we dont have units
of inertia does'nt mean we couldnt if we wanted them. And the other fact
is that if inertia, << the resistance of mass to any change in velocity
>> was not quantifiable... then the force required to change the velocity of any given mass would simply be forced to accept a degree of random resistance... and Newtons second law would fail. I mean you cant have it both ways.  Inertia is a concept on the one hand... and as a concept alone it represents no particular value... just a vague very general defined reference to resistance to change. On the otherhand... this same resistance is so predictably, so quantifiably dealt with by the concept of force. It seems apparent then that Inertia is on the one hand a variable, and on the other hand a value... except that we dont deal with the value part... we dont bother with units of inertia. But I rather suppose we could if we wanted to.

Force could be viewed likewise methinks... if we choose. It could be a
variable... a concept... and as such the idea of force... the property
of force, certainly continues to exist despite the lack of any actual
force. The absence of force does not in any way change its behaviour
when it is present. Mass at rest has inertia. Of course it does... but
it is latent... it isnt resisting anything because there is no force for
it to resist. F = 0, I = 0.  That doesnt mean there is no inertia... it
means a there is no force, and nothing to resist... that there is no
acceleration,,, that the concerned piece of mass is at rest. Equal and
opposite forces are a variation of this same theme. I find nothing in
any text or resource that conflicts with this perspective.

Not that it really matters.... We dont use inertia as a quantity... tho
I rather suspect we could. Ohm :)


> 
> The lead ping pong ball does not in fact have more inertia than the
> regular ping pong ball. However, it does take more force to change its
> direction +/or speed, i.e. its velocity. It takes more force because
> it is more massive, not because it has more inertia. Inertia is "the
> tendency" of a body (an object) to resist a change in its velocity (at
> rest, that velocity is zero). A more massive object doesn't "have"
> more inertia, it has more mass.
> 

Inertia as a tendancy has of course no particular value. But if inertia
is defined as the << resistance of mass to a change in velocity >> and
that same << change in velocity >> if governed by a precisely defined
law such as F = ma, the Inertia becomes more then just a tendancy... it
becomes also a quantity. Tendancy = variable, Quantity = value. A
variable does not cease to exist just because it has under certain
cicumstances 0 as its value.

So... on the one hand... any mass has the exact same tendancy as any
other...towards resisting a change in interia. On the otherhand... it
will actively... actually resist any given change depending on its mass.
Very quantifiably so. If not then F = ma would not work. In fact.. you
could very easily go so far as to say that a mass will offer a given
resistance to a given rate of acceleration.... so much so that F = ma
works out just fine.  Sematics maybe... Moot point maybe too since we
use force units and not Inertia units...  But Inertia simply MUST be
quantifiable... if not... then we simply could not predict how much
force it takes to accelerate to any given rate any given amount of mass.
I dont really see how you can escape that truth.


> Ed Sutton is really trying to steer us in a more fruitful direction
> when he says:
> 
> But what we are trying to do here (I think?), is try to make piano
> actions better for the pianists.
> Since there are so many kinds of pianists, there might be many ways to
> make pianos better, of more adapted to various players and ways of
> playing.
> 
> And in particular, we were concerned with the placement of key leads.
> For a long time many of us have followed the rule of thumb that it was
> better to produce a given front weight by placing a large quantity of
> lead close to the balance rail than by placing a smaller quantity
> close to the front, that this makes the action "feel better" and
> repeat faster, at least in the bass octaves.
> 
> If this is true, then it is worth going to a lot of trouble to do it,
> if not, it is a waste of time.

I think what we are after... is a relationship of front key inertia, to
that of what the key is driving, at the same time getting this to match
the saturation point of a given action. And I think that Mark, and John
are hot on the trail.

> 
> FWIW,
> 
> Alan
> 
> 

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Cheers
RicB