[Phys-L] Re: conservation of angular momentum question

[Daniel Crowe <dcrowe@SOTC.ORG>]

"Torque" and "moment" are synonymous.  A couple is a special type of
torque.

About any origin, there is a torque associated with each force.  If the
line of action of a force passes through the origin, then the torque
associated with that force is zero.

A couple is the net torque associated with two forces that are equal and
opposite.  If the two forces share the same line of action, then the
couple is zero, otherwise it is not.  The magnitude and direction of a
couple are independent of the coordinate system; the magnitudes and
directions of most torques depend on the coordinate system.  A system
acted on by only couples is in translational equilibrium, but it is not in
rotational equilibrium.

Most interesting couples are not associated with interaction pairs
(traditionally, action-reaction pairs), because most interaction pairs
share the same line of action.

On Mon, 14 Mar 2005 22:48:25 -0500, John S. Denker <jsd@AV8N.COM> wrote:

> On 03/14/05 21:57, Daniel Crowe wrote:
> > Just a minor quibble:
> >
> > A pair of (equal and opposite) forces separated by a lever arm is a
> > couple.  There is a nonzero moment (torque) associated with any single
> > force if its line of action doesn't pass through the origin.
>
> Yes, AFAICT it's minor ... but I'd like to understand
> it anyway, and I'm not yet succeeding.
>
> By the third law of motion, there is no such thing as a
> "single force".  So isn't there pretty much a one-to-one
> mapping between torques and couples?
>
> I habitually consider torque synonymous with moment.  It's
> been years since I heard, saw, or used the term couple,
> and I'm not sure if it refers to an important concept.

<snip>
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