Re: joules versus newton.meters

["John S. Denker" <jsd@MONMOUTH.COM>]

At 12:53 PM 1/30/01 -0500, Prof. John P. Ertel (wizard) wrote:
> Units by there very definition cannot be
> other than scalar.  Therefore, I don't understant the difference between
>   "Newton DOT 1 meter"       and       "Newtons CROSS meters"
> It simply makes no sense.  I hope we are not about to embark upon the
> slippery ground that engineers tread where they distinguish between
>   (meters)(newtons)       and        (newtons)(meters)
> the former being units of torque and the latter being units or
> work/energy.

Good points.

Then at 10:22 AM 1/30/01 -0800, Leigh Palmer followed up:
> I think Zach Wolff had a point there, though of course his units are
> highly unconventional. Torque is a pseudovector quantity (or else a
> bivector quantity) and energy is a scalar quantity. Certainly joules
> should not be used as torque units, but no confusion should arise
> if torque is completely specified, including its axial direction,
> since energy is a scalar, with no direction. (The magnitude of a
> torque is not *per se* a physical quantity, any more than the x-
> component of a force is.)

Hmmmmmm.  Ingenious arguments.  Not convincing, but ingenious.

Here's where I come down on this issue:

1) Left to my own devices, I write torques as netwon.meters;  on emotional
grounds I prefer newton.meters to joules.

2) However, emotions are not physics.  The physics says that if I let a
torque of 5 newton.meters act through an angle of 3 radians, I do 15 joules
of work.  Therefore a newton.meter is, in a very physical sense, one joule
per radian.  Shortening this to one joule is perfectly acceptable.

3) The argument about vectors and cross products is not convincing.  A
vector quantity such as a force is conventionally represented as a term
with three factors:
  *) The magnitude
  *) The unit of measurement
  *) A unit-vector in the appropriate direction.

Combining the directional information with the unit of measurement would be
unconventional, and IMHO inadvisable.  When doing dimensional analysis, one
should check the vectorial character of the terms -- in addition to
checking the units of measurement, but these are two separate checks.

By the same token, the units of measurement for a vector component are the
same as for the vector itself.