<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <META content="MSHTML 6.00.2800.1276" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV><FONT face=Arial size=2>Well, I exaggerated the situation for = the sake of emphasis.  Adding lead weights to the keys and/or moving them will = change its moment of inertia.  </FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Will it change very much?  Will = you be able to detect the difference?</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Well, that's why we have engineering = units for m.o.i. (slug-ft^2, or kg-m^2) and a way to calculate it...otherwise we'd = be shooting in the dark.  And if we know the moment of inertia = before and after we add/move the leads, we can calculate a <EM>percent change = </EM>to get a <EM>relative</EM> sense of what's going on.  That way we = don't have to have a "feel" for how much a killogram-meter-squared is.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>So, for example, if we calculate the = m.o.i. with no weights and then calculate it again after we've added weights and the = difference is a 20% increase, we can say that the mechanism is now 20% more = sluggish, which would be much more noticable than if it were 0.01% more sluggish.  Obviously, putting a quarter in the fat kid's pocket is less "noticable" = than putting a bowling ball in his lap.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>You'll just have to do the math and = see.  That's what engineering's all about.  The weights may be small and = the key large, but the key is only wood and uniform; the weights are lead and concentrated away from the pivot point.  You may find out that they = are negligible, or you may find that they have a profound effect.  I'm = guessing that they'll be somewhere in between, but you won't know till you figure = it out.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Don A. Gilmore<BR>Mechanical = Engineer<BR>Kansas City</FONT></DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=ed440@mindspring.com = href="mailto:ed440@mindspring.com">Ed Sutton</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A title=caut@ptg.org href="mailto:caut@ptg.org">College and University Technicians</A> <STRONG>'Subject:</STRONG> Re: What does the moi feel like?</DIV> <DIV><BR></DIV> <DIV><FONT face=Arial size=2>Yes!  And isn't this = "sluggishness" the "MOI" we've been talking about????</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>I know the image of the kids on the teeter-totter.  In fact, I've often used the image of elephants = on the teeter-totter!</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>And I suppose in a blindfold test, I = could tell by pushing if the teeter-totter was empty, or had the elephants in place.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>But here we have been discussing the = merits of placing two leads at the front of the key, or four at the back.  In principle this makes plenty sense, but in practice , we = aren't dealing with anything like the degree of difference between the empty teeter-totter and the one with the kids or elephants.  We are = dealing with very slight differences of key lead placement in piano actions, = where most of the "sluggishness" we feel comes from the = hammers.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>"Sluggishness" is a powerful sounding = word, but in a situation close to the zero friction, zero gravity experiment, do = you think you could distinguish between the key with two leads at the = front and the key with four at the back (located to produce identical = frontweights) by pressing the key with your finger to produce different hammer velocities?</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Ed Sutton</FONT></DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=eromlignod@kc.rr.com = href="mailto:eromlignod@kc.rr.com">Don A. Gilmore</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A title=caut@ptg.org href="mailto:caut@ptg.org">College and University Technicians</A> = </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Monday, January 05, = 2004 9:42 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: What does the = moi feel like?</DIV> <DIV><BR></DIV> <DIV><FONT face=Arial size=2>Hi Ed:</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>All that would be left is the = "sluggishness" of the parts,<EM> i.e</EM>. the tendency of the key not to want to move = and not to want to <EM>stop</EM> moving.  The force = required would be proportional to how quickly you try to change the speed of the = key.  Incidentally, if you totally balance out the weight of the hammer, = the key won't come back up to its starting position.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Think about an ordinary playground teeter-totter.  With no one in either seat, it is easy to move = it around and it stays where you put it.  Now put a fat kid on = either end (both the same weight).  It's still balanced and stays where = you put it, but it is much more difficult to start and stop it.  The = fatter the kids, the more moment of inertia the system has.  To start one = kid upward quickly takes a big heave.  Then if you want to stop him = it is also difficult; in fact, he may actually lift you off the ground if = he has enough energy at that point.  The feel would not be the same at = all for an empty teeter-totter.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Note that since the system is = balanced, any disturbing force can tip the teeter-totter, no matter how small = (neglecting friction).  I can drop a small brick in one kids lap and = start the lever turning and it will accelerate faster and faster until he = strikes the ground.  The key concept to realize is that the teeter-totter = will accelerate at a greater rate if I drop the same brick onto it = when it's empty than with two fat kids sitting in it.  If I put two = 500-lb. slabs of concrete in each seat, the brick will accelerate them even less, = though the system is still balanced. </FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Don A. Gilmore<BR>Mechanical = Engineer<BR>Kansas City</FONT></DIV></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML>