Re: point particles

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

> John, I share your pain!
> Your intuition is thwarted by "the magic of rigid body forces".  These
> forces cause the far (uncharged) end of the rod to pivot so as to keep the
> CM stationary.

Perhaps, but my sense is that it has more to do with a lifetime of
experiences with physical pendula.  I see the upward force on the
charge at the end of the rod and just can't help imagining it as
providing a point of suspension.  It seems like the upward force
applied at that point ought *somehow* (indeed, via rigid body forces)
to pull the CM over toward it the same way the CM of a physical
pendulum gets pulled over toward a point underneath the point of
suspension.

It's much harder to imagine the center of mass as an effective "point
of suspension" if only as a result of the fact that the gravitational
force "applied there" is *downward*!  It gets easier, but still not
quite transparent, if I imagine the rod to be "suspended" BY gravity
AGAINST the upward electric force.  I still can't quite shake the
faulty intuition that the rod ought to oscillate about a point
somewhere between the CM and the end with the point charge.

Of course, the two situations are quite different.  First of all, the
point of suspension for a physical pendulum does provide a vertical
suspending force, but its magnitude oscillates with a period half
that of the pendulum.  More importantly, it also provides a
horizontal force that oscillates from side to side with a period
equal to that of the pendulum and that, of course, explains the side
to side motion of the CM.

> I was long bothered by the magic of rigidity. EG: how does a force get
> multiplied across the fulcrum of a lever?
>
> I finally quieted my intuition by using Interactive Physics to model a lever
> with a system of  masses and springs (monitoring the spring/applied forces
> on each mass) in a myriad of situations.  The results, evolving in time
> through damped oscillations, directly show the evolution of these forces and
> the subsequent motion of the (semi-rigid) object.

I second this emotion.  Playing with IP is one of the best ways I
know to test and sharpen intuition.  I can't count the number of
times I have been surprised and then enlightened by something I have
discovered fiddling around with IP.

It's too bad the publisher has IMO treated IP's user base SO poorly.
First they charged too much for a product that, at a more reasonable
price point would have quickly become established as an essential
element in the toolbox of virtually every physics instructor in the
world.  In more recent years the new publisher has milked IP users
with outlandish fees for "major releases" (to judge by the change in
version number) that turn out to have relatively minor and usually
only superficial improvements.

> Since I retired, I no longer have access to IP (the school's).  Now you have
> so peaked my interest that I am going to order my own copy of IP and play
> further!  Go thou and do likewise (play)  : > )

Hmm...  Retirement or access to IP? ...  Don't torment me.

--
John Mallinckrodt        mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm