Re: Newton's 3rd law? was Re: inertial forces (definition)

[Bob Sciamanda <trebor@VELOCITY.NET>]

Hi John,
I agree with your disdain for the "centripetal" terminology.  I use the
terms "speed affecting force component" and  "turning force component".  I
try to instill notions like:  1) any force component along the direction
of the velocity will affect the speed and not the direction of motion; 2)
any force component perpendicular to the velocity vector will turn the
direction of the motion and will not affect the speed.  If these visual,
qualitative dicta are instilled, the quantitative statements will be more
user friendly.

(In a calculus-based class I will show the general mathematical theorem
that if the time derivative of a vector - which is another vector -  is
presently perpendicular to the original vector, then the magnitude of the
original vector is not changing in time at the present instant.)

Real and gedanken experiments can dramatically illustrate this - eg., hit
a rolling bowling ball from the front, the rear, directly from the side,
and then obliquely from the side.

Your last remark illustrates that this decomposition is most useful when
the statement of the problem includes a disclosure of the center and
radius of curvature at the relevant instant.  But even if not always
useful it is always a valid decomposition of the net force on a particle
and is to me of theoretical/aesthetic value.

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

----- Original Message -----
From: John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, October 25, 1999 2:01 AM
Subject: Re: Newton's 3rd law? was Re: inertial forces (definition)


> On Sun, 24 Oct 1999, Bob Sciamanda wrote:
>
> > I sincerely feel that the problem with student mis-interpretations of
> > F_c=mv^2/r would be eliminated if, after treating the special case of
> > circular, constant speed motion the general case would be presented
and
> > hammered home with copious examples (most texts don't do this).  It
should
> > then become clear that a very useful case of the (oft' used) pair
> >
> > F_x=mA_x;  F_y=mA_y      is the pair
> >
> > F_t=mdv/dt;  F_c=mv^2/r;
> >
> > ... I can say that I have never experienced this misconception as even
a
> > minor epidemic problem. ...
>
> I agree with what I see as the thrust of your comments here, but I think
> it pays to use different terminology like "tangential and transverse" or
> "parallel and perpendicular" as someone else pointed out a few days ago.
> "Centripetal" implies the existence of a "center" that is far from
obvious
> in the general case.  The term is just too loaded and too often abused
for
> my taste.  I can only accept your statement that you've never
encountered
> any major conceptual difficulties associated with the term; but I know
> that I have.
>
> I will point out, however, that in the fully three dimensional case,
this
> approach might become a bit less compelling as the precise direction of
> the transverse or perpendicular component of F can become far less
> obvious.
>
> John Mallinckrodt      mailto:ajm@csupomona.edu
> Cal Poly Pomona          http://www.csupomona.edu/~ajm