In the book Surely You Are Joking, Mr. Feynman! Richard Feynman tells a story of a Cornell cafeteria plate being tossed into the air. As the plate spun, it wobbled. Feynman noticed a relation between the two motions. He solved the motion of the plate by using the Lagrangian approach. This solution didn’t satisfy him. He wanted to understand the motion of the plate by analyzing the motion of its individual particles and the forces acting on them. He was successful, but he didn’t tell us how he did it. We provide an elementary explanation for the two-to-one ratio of wobble to spin frequencies, based on an analysis of the motion of the particles and the forces acting on them. We also demonstrate the power of numerical simulation and computer animation to provide insight into a physical phenomenon and guidance on how to do the analysis.
REFERENCES
1.
Richard P.
Feynman
, Surely, You Are Joking, Mr. Feynman!
(Norton
, New York, 1997
), pp. 173
–174
.2.
James
Gleick
, Genius: The Life and Science of Richard Feynman
(Vintage
, New York, 1992
), pp. 227
–228
.3.
The original Feynman’s story, as told in Ref. 1, has a twist: Feynman states the plate spins twice as fast as it wobbles, while in truth it wobbles twice as fast as it spins. Whether his error was a mere slip in memory, or another practical joke meant for those who do physics without experimenting, is not known. The argument based on Euler’s equations of rigid body motion proving that Feynman was wrong is given by
Benjamin Fong
Chao
, “Feynman’s dining hall dynamics
,” Phys. Today
42
(2
), 15
(1989
).Similar reasoning can be found in
Jagdish
Mehra
, The Beat of a Different Drum: The Life and Science of Richard Feynman
(Oxford U.P.
, New York, 1994
), pp. 179
–180
.4.
One treatment of the plate based on the analysis of motion of its representative particles was provided by
J. C.
Martinez
, “Force-free precession of a spinning plate
,” Eur. J. Phys.
13
, 142
–144
(1992
).Very interesting insights to the problem of particles motion can be found in
P. L.
Edwards
, “A physical explanation of the gyroscope effect
,” Am. J. Phys.
45
, 1194
–1195
(1977
).5.
The differential equations obtained from the Lagrangian for the plate can be found in the material mentioned in Ref. 6.
6.
See EPAPS Document No. E-AJPIAS-75-001702 for the computer model of the plate (Java applet), simple tutorials for students’ active explorations in the form of exercises where students need to interact with the applet that provides direct experience and support in better understanding of concepts and related behavior. The materials and the paper assume only knowledge at an introductory mechanics level. Advanced technical materials meant for teachers or students familiar with advanced mechanics subject, the theory of rigid body, provide a connection between our elementary explanation and the standard approach of the rigid body theory based on Euler’s equations. This document can be reached via a direct link in the online article's HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html).
7.
The initial orientation of the plate in the applet is given by the Euler angles , , and , as defined in
Herbert
Goldstein
, Charles
Poole
, and John
Safko
, Classical Mechanics
, 3rd ed. (Addison-Wesley
, New York, 2002
), Sec. 4.4. Correspondingly, the initial motion of the plate is represented by rates of change , , and .8.
The alternative quantitative proof based on vector algebra is presented as a tutorial in Ref. 6.
9.
Calculation of the integrals is straightforward and is included in the problems given in Ref. 6.
10.
See for example
David J.
Morin
, There once was a classical theory…, Introductory Classical Mechanics with Problems and Solutions, Sec. 8.6. available at ⟨http://isites.harvard.edu/fs/docs/icb.topic58975.files/old-book/ch8.pdf⟩, orL. N.
Hand
and J. D.
Finch
, Analytical Mechanics
(Cambridge U.P.
, Cambridge, UK, 1998
), p. 296
, orJohn R.
Taylor
, Classical Mechanics
(University Science Books
, Sausalito, CA, 2004
), Sec. 10.8.© 2007 American Association of Physics Teachers.
2007
American Association of Physics Teachers
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