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: MOMENT OF INERTIA



On Fri, 18 Dec 1998, Martha Takats wrote:

Dan M's energy-conservation derivation is the one I use (so I don't
have to worry about rotation about a moving axis, or an axis that
isn't through the center of mass, etc.). But I still worry about why
there are no non-conservative forces doing work--for example the force
of static friction, which prevents slipping. Can anyone give a SIMPLE
explanation of why we don't have to include it in the work-energy
equation?

(Warning: The following is intended only for those interested in
pursuing this matter carefully. All others are encouraged to push
the delete key now.)

Martha,

It depends on *which* work-energy equation you are referring to
and, in some cases, which reference frame you are using for your
calculations. If, for instance, you use the one that Bob Sciamanda
often refers to--the one that equates the integral of the net force
dotted with the displacement of the CM to the change in the
translational kinetic energy--then you *do* have to include the
force of friction simply because the CM moves (at least in the frame
of the incline.) If you use the one that is more commonly employed
in situations such as these--the one that equates the sum over all
forces of the *individual* integrals of each force dotted with the
displacement of the point of its application to the change in the
total energy--then you don't have to include the frictional
force because its point of application does not "move" (at least in
the frame of the incline) although it does "change."

In our paper, "All About Work" (AJP, Vol. 60, pp. 356-365, 1992,
yes, here I go again), Harvey Leff and I provide seven different,
useful definitions for work and determine their relationships to
various changes in system energies. Referring to Table 1 from
that paper, I find that

no work is done by friction (in the frame of the incline) under
the first two definitions (with the second definition
corresponding to the version that you and Dan use),

no work is done (period) under the third and seventh definitions,

work is done (in the frame of the incline) under the fourth
(which corresponds to the version I have linked with Bob
Sciamanda--properly, I hope), and

work is done (period) under the fifth and sixth.

John
-----------------------------------------------------------------
A. John Mallinckrodt http://www.csupomona.edu/~ajm
Professor of Physics mailto:ajm@csupomona.edu
Physics Department voice:909-869-4054
Cal Poly Pomona fax:909-869-5090
Pomona, CA 91768-4031 office:Building 8, Room 223