We discuss the controversy about the demonstration of the law of the lever as given by Archimedes. One aspect of the discussion concentrates on the meaning of the postulates which he utilized. We analyze what consequences would arise if nature behaved in such a way that the lever followed a generalized power law. In particular, we consider the cases of a torque independent of the distances of the bodies to the fulcrum, proportional to these distances, and quadratic in the distances.

Topics
Educational aids, Educational assessment, Physicists, Public policy and governance
1.
E. J.
 
Dijksterhuis
,
Archimedes
(
Princeton U. P.
,
Princeton
,
1987
), pp.
289
and
305
. Translated by C. Dikshoorn.
Google Scholar
Crossref
Search ADS
 
2.
Archimedes
,
The Works of Archimedes
(
Dover
,
New York
,
2002
), p.
192
. Translated and edited by
T. L.
 
Heath
.
Google Scholar
 
3.
Reference 1, pp.
309
and
311
.
4.
Reference 1, pp.
286
–
287
.
5.
T.
 
Heath
,
A History of Greek Mathematics, Vol. II: From Aristarchus to Diophantus
(
Clarendon
,
Oxford
,
1921
), pp.
24
,
302
,
350
–
351
, and
430
.
Google Scholar
 
6.
Reference 2, pp.
clxxxi
–
clxxxii
.
7.
P.
 
Duhem
,
The Origins of Statics
(
Kluwer
,
Dordrecht
,
1991
), pp.
264
–
267
,
457
–
465
, and
307
. Translated by G. F. Leneaux, V. N. Vagliente, and G. H. Wagener.
Google Scholar
Crossref
Search ADS
 
8.
W.
 
Stein
, “
Der Begriff des Schwerpunktes bei Archimedes
,”
Quellen und Studien zur Geschichte der Mathematik, Physik und Astronomie. Abt. B: Quellen
 
I
,
221
–
244
(
1930
).
Google Scholar
 
9.
Reference 1, pp.
17
,
47
–
48
,
289
–
304
,
315
–
316
,
321
–
322
, and
435
–
436
.
10.
A. K. T.
 
Assis
,
Archimedes, the Center of Gravity, and the First Law of Mechanics
(
Apeiron
,
Montreal
,
2008
), pp.
72
and
97
–
105
. Available at ⟨www.ifi.unicamp.br/~assis⟩.
Google Scholar
 
11.
E.
 
Mach
,
The Science of Mechanics—A Critical and Historical Account of Its Development
, 6th ed. (Open Court, La Salle,
1960
), pp.
19
–
20
. Translated by J. McCormack.
12.
Reference 1, pp.
289
–
304
.
13.
Reference 10, Sec. 9.7, pp.
177
–
185
.
14.
Reference 1, p.
288
.
15.
Archimedes
,
Die Quadratur der Parabel und über das Gleichgewicht ebener Flächen oder über den Schwerpunkt ebener Flächen
(
Akad. Verlagsgesellsch
,
Leipzig
,
1923
). Vol.
203
of
Ostwald’s Klassiker der exakten Wissenschaften. Übers. u. mit Anmerkungen vers. v. A. Czwalina-Allenstein
.
Google Scholar
 
16.
Reference 1, p.
294
.
17.
Reference 1, p.
311
.
18.
Reference 10, pp.
182
–
185
.
© 2009 American Association of Physics Teachers.
2009
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.