Re: cavendish expt

[Brian Whatcott <betwys@DIRECTVINTERNET.COM>]

At 02:14 PM 12/5/02, John Denker, you wrote:
> /snip/
> So what I said was true: a solid cylindrical fiber
> has the minimal torsional stiffness for a given
> tensional strength (assuming constant length in
> the Z direction).
> /snip/

?

It will help to consider torsional suspensions of two
cross-sections:
a solid rectangular shape like a tape and a solid square.

Label the length of the square section's side as  h units
and label the lengths of the long side of the rectangle section
 as h units and the thin side as b units;
then the respective torsional resisting moments
are given by
Rectangular: 2/9 b^2 h
Square:         2/9 h^3

For a cross section area of  1000 units of area in each section,
the rectangular section of 1 X 1000 length units has a torsional resisting
moment
of 2/9 * 1000
the square section of 31 X 31 length units has a torsional resisting moment of
2/9 * 31^3 = 2/9 * 32,000

Hence it may be said that a tape is 32 times less torsionally stiff
than a square rod of the same c/s area.

A similar result applies to solid rods of circular section: much stiffer
torsionally, than a tape of the same cross section area.

This is the thrust of Bernard's note - though I avoided the term 'cylinder'
which can suggest the stiffer annular cross section, rather than the less
stiff
solid round rod of constant areas.
Brian Whatcott
  Altus OK                      Eureka!