Re: Rotation problem

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

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