Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-L] treating force as a vector ... consistently



I have a question about this thread. I am trying to put together some
thoughts about force-as-vector, bound vector, etc. I've never worked with
(or thought I needed to work with) "bound vectors". But before I venture
an opinion,I have a question:

A force is a vector. It has magnitude and direction. I am not ready to
ask if it has a "point of application". (I believe that the point of
application exists. I just don't know that it is a property of the force.)
So I guess my question is: can a force have ANY other property or
information assigned to it other than magnitude and direction? It's a
vector, but is that all it is? In particular, where does the information
exist that tells us which object a particular force is acting on? Not
"where" but "on what"? The information has to exist somewhere. When we
apply Newton's 2nd law to a particular object, we do somehow know to limit
ourselves to forces acting on that particular object. Those are the only
forces we draw on the free-body diagram. Is the thing that associates a
force with the object a property of the force?

(If this seems angel-on-pin, feel free to ignore. I think the thread is
interesting and legitimate even if it raises questions I would not feel the
need to discuss in class.)

On Thu, Sep 15, 2016 at 5:47 PM, David Craig <craigda@lemoyne.edu> wrote:


On 09/13/2016 11:57 AM, John Denker wrote:

Yes, but first things first. When the audience doesn't have a
firm grasp of what a vector is, or how a vector field differs
from a vector space, you can't start with tangent bundles.

In fact a tangent bundle is defined in terms of tangent spaces,
so it makes sense to do tangent spaces before tangent bundles.

There is a rather general pedagogical principle that says "concept
before name". You can teach people pretty much everything they
need to know about tangent bundles without ever using the word.

Settle down, John. I was just giving it the proper name for those who
care about such things. I didn’t bring it up — you did.

One is free to dismiss it if you like, but when you are doing things
like GR it really is a useful idea.

That's ambiguous, due to a dangling antecedent. Does "it” refer to
rooted vectors, or to fiber bundles?

Seriously? You definitely have too much time on your hands ;-)

All in good fun. I always enjoy reading your posts, even if I haven’t
the time to engage them.

David Craig


<http://web.lemoyne.edu/~craigda>



_______________________________________________
Forum for Physics Educators
Phys-l@www.phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l