<!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 background=""> <DIV><FONT face=Arial size=2>Hi Don,</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2><<Thirdly, the dynamic motion of = the hammer has been described herein as a linear problem, which it is not. >></FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Ah, yes, true.  However, the same = sorts of principles most of us have been arguing apply equally to linear and = angular systems.  If linear systems are so hard for everyone to = understand, angular systems would make most people's brains bleed!  It's = perhaps more useful, I think, when talking about transfer of energy from one = component to another to another to another, to pretend like we're talking about a = linear system, even though it really ain't so.  At least then it's = possible to see how energy is lost in the system, which was really my only point in the = first place -- before I got mired down in this whole thing.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>But since you raise the point, = k</FONT><FONT face=Arial size=2>inetic energy for a point mass "orbiting" = rotating about a point can also be described as (mv^2)/2.  Also, velocity is = angular velocity times radius, torque is tangental force times radius, = etc.  S</FONT><FONT face=Arial size=2>o it's really not so different from = a linear system, is it?  Granted, angular moments of inertia are useful for describing rotation of complex mass distributions, but for describing = something like a key lead, which is almost a point mass, aren't linear terms = really close enough?  If my physics professors had asked us to describe the = kinetic energy of a roller coaster in angular terms, using the radii of curves = in the track and "torque" exerted by gravity, I think there would = surely have been a mutany!  ;-)</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Peace,</FONT></DIV> <DIV><FONT face=Arial size=2>Sarah</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2></FONT> </DIV></BODY></HTML>