I think what Jim's saying is there needs to be a "connection" between the
vector definition of torque and the vector definition of rotation.
Fortunately there is this connection, in that rotation has a rotational
velocity and rotational acceleration, both of which have the same vector
direction. So torque is defined by its right-hand-rule, and rotational
acceleration defined by its right-hand-rule, such that the two are in the
same direction and related by a simple scalar constant: the moment of
inertia!
>>>and in rotational form as
>>> a = T / I
Sorry this is getting off-topic, but this group is devoted to good
measurement practice and physics handles this very elegantly.
Nat
Now back to product labels, state DOT's, and UK loose goods regulations! <g>
> 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
> >
> >
>
>
>
