TITLE: Basic aspect of relativistic rotation: Franklin rotation of a sphere
AUTHOR: Ben-Amots, N.
SOURCE: Foundations of Physics, v. 33, No. 9 , pp. 1369-1372 ( September 2003).
ABSTRACT: We give a relativistic treatment to the dynamics of spherical
bodies rotating at very
high speed. It is found that most of the mass of a
homogeneous spherical quark with Franklin
rotation, is due to the
relativistic increase of the mass.
9 references:
Franklin, P., "The meaning of rotation in the special theory of
relativity,"
Proceedings of the National Academy of Sciences of the
USA, v. 8, pp. 265-268 (1922)
and more 8 references.
KEY WORDS: relativity; Franklin rotation; relativistic mass.
COMMENT: Lectured 25.6.2002 in
IARD2002 Conference
.
Cited by
Oziewicz, Zbigniew
"Rival theories of relativity: Groupoid relativity versus Lorenz-group relativity,
Non-reciprocal velocity versus reciprocal velocity" (129 pp.)
Short background:
Philip Franklin (1898-1965) was the first to recognize that in relativistic
rotation the
Newtonian formula
v=ω r
is not valid. Instead, Franklin showed (1922) that for relativistic rotation
the correct
formula is:
v=c tanh(ω r/c)
Franklin's formula obeys the requirement of relativity that the
circumferential velocity
v never exceeds the velocity of light c,
for any radius r and
angular velocity ω.
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