Re: Rotation problem

["Lemmerhirt, Fred" <FLemmerhirt@MAIL.WCC.CC.IL.US>]

Just in case anyone else is trying to interpret my question about the
"falling H":  There seems to be no contradiction in this problem after all
(and thus no need for the "ad hoc rule" I mentioned).

Thanks to John Mallinckrodt for quickly interpreting and clarifying this
without the text reference or even a diagram.  (PHYS-L is a great resource
for us in one-person departments who have no one nearby to consult about
little things like this.)

______________________________________________________
Fred Lemmerhirt
flemmerhirt@mail.wcc.cc.il.us
http://chat.wcc.cc.il.us/~flemmerh/physics.html
Waubonsee Community College      Sugar Grove, Illinois




> -----Original Message-----
> From: John Mallinckrodt [SMTP:ajmallinckro@CSUPOMONA.EDU]
> Sent: Friday, December 03, 1999 6:12 PM
> To:   PHYS-L@lists.nau.edu
> Subject:      Re: Rotation problem
>
> I'm not totally that I understand what problem you are trying to address
> with your ad hoc rule (and I don't have a copy of the text), but perhaps
> the following will help:
>
> Suppose the "H" is made of 3 identical rods each with mass M and length L.
> If your "system" is the two nonaxial rods, then the mass of the system is
> 2M and the center of mass falls by 3L/4.  If your system is all three
> rods then the mass of the system is 3M and the center of mass falls by
> L/2.  In *either* case, the gravitational potential energy decreases by
> 3MgL/2 and that energy shows up as rotational energy of (1/2)Iw^2 =
> (1/2)(4ML^2/3)w^2 giving w =  (3/2)(g/L)^(1/2).
>
> John
>
> On Fri, 3 Dec 1999, Lemmerhirt, Fred wrote:
>
> > There is an old familiar rotation problem with which I am currently
> uneasy,
> > and about which I am hoping to get some advice.  It involves an H-shaped
> > "frame" falling from a horizontal to a vertical position about an axis
> along
> > one side of the H.  In Halliday, Resnick & Walker's Fundamentals, 5th
> ed.,
> > it is Problem 83 in Chapter 11.  In order to solve for the angular speed
> in
> > the vertical position by a simple energy method it seems necessary to
> > introduce an ad hoc rule something like:  "Any mass that contributes
> nothing
> > to the rotational inertia should be excluded from the center-of-mass
> > calculation."  (Such a rule is not needed if the analysis is done for a
> > parallel axis a distance x along the crossbar of the H and then x is set
> > equal to zero.)  Has anyone developed a satisfying way of dealing with
> this
> > problem?  (Or can someone tell me that I'm just being obtuse and
> overlooking
> > something fundamental?)
>
> John Mallinckrodt      mailto:ajm@csupomona.edu
> Cal Poly Pomona          http://www.csupomona.edu/~ajm