20080404, 12:16  #1 
"Lucan"
Dec 2006
England
1100101001010_{2} Posts 
Rotating cylinder
Since Mally departed this world there has been a dearth of
simple and/or physicsrelated puzzles. As an exteacher 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 20080404 at 12:28 
20080404, 13:37  #2  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2·5·677 Posts 
Quote:
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"? 

20080404, 14:36  #3 
Oct 2006
2^{2}·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 highspeed 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. 
20080404, 18:33  #4 
"Lucan"
Dec 2006
England
194A_{16} 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 20080404 at 18:43 
20080407, 03:48  #5 
"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. 
20080407, 04:49  #6  
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
Quote:
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 20080407 at 05:01 

20080408, 22:36  #7 
6809 > 6502
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Aug 2003
101×103 Posts
2·3·11·167 Posts 

20080409, 01:12  #8  
"Lucan"
Dec 2006
England
194A_{16} Posts 
Quote:
I think the use of carbon fibre tallies with my finding that maximum energy density ~ breaking stress (tensile strength) 

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