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I'm confused about this discussion too...
2) I think we all agree that in many situations when dealing
with a force, we need the idea of direction-and-magnitude of
the force and also the idea of point-of-application .....
Agreed. And to your point about viewing the angular momentum L as
(d/dt) of the torque T, I would expect what follows below to apply to
both L = r x p and T = r x F.
I [either sheepishly or sadly, not sure which] never heard of a
bound vector until this discussion.
The question is simply whether we want to express those two
things using one "vector" (i.e. a so-called bound vector)
or using two vectors (i.e. plain old vectors, aka free
vectors).
Eh? Based on the wiki article you cited, a bound vector "possesses a
definite initial point and terminal point." By this simple reading,
both r and F qualify.
I [either sheepishly or sadly, not sure which] never heard of a
bound vector until this discussion. Does it satisfy someone's need to
formalize this stuff to the nth degree, or does it serve a useful
purpose?
My reading of the math and physics literature going back 50+
years is that vector means free vector exclusively, so that
a so-called "bound vector" is not really a vector at all, but
rather a pair of vectors, like two persons inside a horse
costume.
Are you saying that you would view r x F as one bound vector
consisting of a pair of free vectors r and F?
I don't see any advantage, much less any necessity, but I *do* see
much potential for needless confusion in trying to distinguish
between "bound" and "free" vectors. Vectors have magnitude and
direction. They do not have "location." The standard "position
vector" locates a specific point in space relative to some origin by
having a magnitude and a direction such that, *if* its tail is
positioned at the origin, its tip will be at the desired point.
Am I missing something?