I haven't seen the term used explicitly, but it seems to appear in the definition of a torque as a cross product r X F. The vector r is determined by the so-called point of application of the F relative to the origin.
For a point object it is clear that the r in the angular momentum is to the position of the point particle - so the vector p is not required to be bound. For an extended object, we have the choice of adding the angular momenta of all the point objects that we assume the total object is made of (requiring no bound vectors), or we can use the angular momentum of the center of mass (rcm X ptotal) and add to it the angular momentum of the point objects about the center of mass. In the second approach the ptotal vector is still not really bound to the CM - since the CM is independently defined.
At first blush it appears that the concept of a bound vector is not required for angular momentum, but it is useful for torque.
Bob at PC
________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker [jsd@av8n.com]
Sent: Sunday, September 05, 2010 1:04 PM
To: Forum for Physics Educators
Subject: [Phys-l] bound vectors ... or not
This came as a surprise to me. I am 99.99% certain the
notion of "bound vector" does not appear in any of my math
books. I don't recall seeing it in any of my physics books.
I don't recall hearing any physicist utter the term or use
the concept.
The concept of "bound vector" definitely exists in the minds
of students, even if they don't can't give a name to it.
In particular, I call attention to the idea of expressing
Newton's third law in terms of bound vectors. I'm not saying
this is a /good/ idea, but it's not completely crazy.
One problem with bound vectors is that they are incompatible
with the mathematical definitions of vector and vector space.
And as far as I can tell, the tradition within physics for
at least the last 50 years is to stick with the mathematical
definition of vector and vector space, i.e. to use "free"
vectors for everything. In particular, in Newton's laws,
the force and the point of application are two different
vectors. To quantify the third law, it suffices to assert
conservation of the bivector r/\p (angular momentum). Then
conservation of the vector p (momentum) is obtained as a
corollary, as you can see by choosing a far-far-away datum
(origin) for defining the lever arm (r).
However ... I would like to throw this open as a question to
the group.
-- Can anybody cite an example of "bound vectors" appearing
in a reputable physics text?
-- As a matter of policy going forward, is there any advantage
to introducing "bound vectors" into the physics curriculum, or
should should stick with the mathematicians' definitions of
vector and vector space?