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...if you take a tube and slit it
lengthwise, forming a C-shaped cross section, you
unstiffen it tremendously, converting it from
something stiffer than a solid rod to something
floppier than a solid rod.
For a sold rectangular cross section of width w and
thickness t, the torsional spring constant goes like
K ~ M t^3 w / L (1)
where M is some modulus, with dimensions of stress
(same dimensions as pressure).
BUT!!! For the Cavendish experiment, equation (1)
is a red herring!!!!
If you do the physics (which requires nothing
more than high-school geometry and the principle
of virtual work) you find that the torsional
restoring force constant goes like
K' ~ M' t w^3 / L (2)
which is verrrry different from equation (1).
Approximating M'=M, the two equations differ by
a factor of w^2/t^2 and some minor dimensionless
constants. For videotape, w is millimeters and
t is microns, so the St. Venant contribution is
smaller by a factor of a million or so.
This agrees fully with my intuition.
Prof. Cavendish wasn't an idiot. He had a good
reason for designing his apparatus to use a
long thin fiber.