Jim:
I'm not questioning torque as a vector. I already know it is. (I still have
my 1950s-vintage Methuen's Physical Monograph on Vector Analysis, by B.
Hague. <g>) My issue was only with defining axis as a vector.
All you have really said is that the cross product of a vector on the x-axis
and a vector on the y-axis is a vector on the z-axis. Pardon my confusion,
but I still don't see that it makes the axis itself a vector.
I accept the convention Nat cites. However, I have difficulty accepting,
from a mathematical point of view, that it's anything more than a convenient
short form. Am I missing something? Am I going dotty or have I got my
vectors crossed? Should I just curl up and div?
Bill Potts, CMS
San Jose, CA
http://metric1.org [SI Navigator]
> -----Original Message-----
> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On
> Behalf Of James R. Frysinger
> Sent: January 03, 2001 15:08
> To: U.S. Metric Association
> Cc: U.S. Metric Association
> Subject: [USMA:10212] Re: Torque & Re: Re: South Africa
>
>
> The convention arises from mathematics, Bill. Torque is defined as a
> cross product. Using T for torque (normally tau is used) and X for the
> cross-product operator,
> T = r X F
> Necessary to this is the convention that radius points outward from the
> center of action. Also, mathematics establishes the direction of a cross
> product such that if one were to cross the x-axis unit vector into the
> y-axis unit vector, the z-axis unit vector results. This defines our
> "right-hand coordinate system" which is based on the "right-hand rule",
> again, a mathematics convention.
>
> One can write this in a nifty manner using matrices but I don't feel
> like messing with it here and I suppose very few here would really care
> to see it! Those that do can consult any introductory calculus text or
> physics text. ;-)
>
> I have never learned of nor have I seen any definition for the
> reciprocal of a vector, by the way, but I'm not a mathematician.
>
> Jim
>
> Bill Potts wrote:
> >
> > Nat Hager wrote:
> > > It's a convenient formalism used in rotational mechanics.
> >
> > For those of us who are not practitioners of rotational
> mechanics, it's a
> > somewhat inconvenient formalism, as it violates the usual mathematical
> > definition of vector.
> >
> > However, thanks for adding to my relatively limited knowledge
> of that field.
> > <g>
> >
> > Bill Potts, CMS
> > San Jose, CA
> > http://metric1.org [SI Navigator]
>
> --
> Metric Methods(SM) "Don't be late to metricate!"
> James R. Frysinger, CAMS http://www.metricmethods.com/
> 10 Captiva Row e-mail: [EMAIL PROTECTED]
> Charleston, SC 29407 phone/FAX: 843.225.6789
>
>
