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 2008-04-04, 12:16 #1 davieddy     "Lucan" Dec 2006 England 11001010010102 Posts Rotating cylinder 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. Last fiddled with by davieddy on 2008-04-04 at 12:28
2008-04-04, 13:37   #2
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

2·5·677 Posts

Quote:
 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"?

 2008-04-04, 14:36 #3 roger     Oct 2006 22·5·13 Posts 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.
 2008-04-04, 18:33 #4 davieddy     "Lucan" Dec 2006 England 194A16 Posts 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 Last fiddled with by davieddy on 2008-04-04 at 18:43
 2008-04-07, 03:48 #5 davieddy     "Lucan" Dec 2006 England 2·3·13·83 Posts 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.
2008-04-07, 04:49   #6
davieddy

"Lucan"
Dec 2006
England

2·3·13·83 Posts

Quote:
 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?

Last fiddled with by davieddy on 2008-04-07 at 05:01

 2008-04-08, 22:36 #7 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 2·3·11·167 Posts
2008-04-09, 01:12   #8
davieddy

"Lucan"
Dec 2006
England

194A16 Posts

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

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