Rotating cylinder

[davieddy]

Since Mally departed this world there has been a dearth of
simple and/or physics-related puzzles.
As an ex-teacher of able pupils, I set this one and
was disappointed to find no takers:
How fast can you rotate a cylinder before it disintegrates?

David

It is important because it is/was a serious suggestion
for storing energy.

[retina]

Originally Posted by davieddy

Since Mally departed this world there has been a dearth of
simple and/or physics-related puzzles.
As an ex-teacher of able pupils, I set this one and
was disappointed to find no takers:
How fast can you rotate a cylinder before it disintegrates?

David

It is important because it is/was a serious suggestion
for storing energy.

For a cylinder made of wet paper, not very fast. For a cylinder made of high tensile steel, a lot faster.

Don't you need to define a little bit more? Or are you wanting some sort of general formula based upon tensile strength, moments of inertia, etc.?

How are you defining "disintegrates"?

[roger]

As far as I remember, when you spin something, it begins to wobble towards the edges. Spinning it fast enough will result in a wobble so massive that it breaks apart due to the forces. I've seen this in high-speed motion capture of various rotating and/or breaking objects

I think retina is correct, tensile strength and moments of inertia will play into the general formula, as well as speed and possibly weight.

[davieddy]

Making your own simplifying assumptions can be counted as
part of the problem (e.g. no wobbling). I expect the angular speed at
which rupture occurs to involve tensile strength, density and
radius. Dimensional analysis will immediately give you a useful
qualitative answer.
A fuller anaysis involves considering the radial and tangential
strains.

David

[davieddy]

Having thought more about it, I was hoping to formulate
a 2D problem in elasticity, but even this is tricky.

A simpler (but related) problem is finding the stress in
a ring of radius r and density d rotating about its axis
with angular velocity w.

[davieddy]

Originally Posted by davieddy

A simpler (but related) problem is finding the stress in
a ring of radius r and density d rotating about its axis
with angular velocity w.

By Newton's 2nd law:
stress*Area*(x/r) = (Area*x*d)*w^2*r (for small length x)

stress=speed^2*density=2*energy per unit volume)

That's cute isn't it?

[Uncwilly]

Of interest:
http://www.utexas.edu/research/cem/c...20testing.html

[davieddy]

Originally Posted by Uncwilly

Of interest:
http://www.utexas.edu/research/cem/c...20testing.html

Indeed. THX.
I think the use of carbon fibre tallies with my finding that maximum
energy density ~ breaking stress (tensile strength)