Intuition suggests that twisting a cylinder will shorten it, but here it is shown that for a cylinder of an incompressible material, like rubber, twisting will always produce elongation.
REFERENCES
1.
Encyclopedia Britannica
, edited by
H.
Chisholm
, 11th ed. (
Cambridge U.P
.,
Cambridge
, 1911
), Vol.
12
.2.
C.-A.
Coulomb
, “
Recherches théoriques et exp érimentales sur la force de torsion et sur l'élasticité des fils de metal
,” Hist. Acad. R. Sci.
87
, 229
–269
(1784
).3.
J. H.
Poynting
, “
On pressure perpendicular to the shear-planes in finite pure shears, and on the lengthening of loaded wires when twisted
,” Proc. R. Soc. A
82
, 546
–559
(1909
).4.
R. S.
Rivlin
, “
Torsion of a rubber cylinder
,” J. Appl. Phys.
18
, 444
–449
(1947
).5.
L. R. G.
Treloar
, “
The elasticity of a network of long-chain molecules
,” Trans. Faraday Soc.
39
, 36
–41
(1943
).6.
J. H.
Poynting
, “
The changes in length and volume of an Indian-rubber cord when twisted
,” India-Rubber J.
October 4
, 6
(1913
).7.
C.
Truesdell
and
W.
Noll
, The Non-Linear Field Theories of Mechanics
(
Springer
,
Berlin
, 2004
).8.
R. W.
Ogden
, Non-Linear Elastic Deformations
(
Ellis Horwood
,
Chichester
, 1984
); reprinted by Dover (1997
).9.
B.
Allen
, “
From the simple to the surprisingly complex—An incremental study of elasticity
,” Phys. Teach.
57
, 570
–571
(2019
).10.
I.
Bruce
, “
The elastic constant of a rubber tube
,” Am. J. Phys.
60
, 157
–160
(1992
).11.
E. P.
Papadakis
, “
Undergraduate experiment on elasticity of rubber bands
,” Am. J. Phys.
31
, 938
–939
(1963
).12.
V.
Balbi
,
A.
Trotta
,
M.
Destrade
, and
A. N.
Annaidh
, “
Poynting effect of brain matter in torsion
,” Soft Matter
15
, 5147
–5153
(2019
).13.
KC Seals
. Material Properties: General Purpose NBR (N70, Nitrile 70 Duro, Buna), <https://kcseals.ca/uploads/images/pdfs/NBR_70.pdf>.© 2020 American Association of Physics Teachers.
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