From: edprochak@gmail.com   
      
   On Friday, March 9, 2018 at 2:59:51 AM UTC-5, John Heath wrote:   
   > On Wednesday, March 7, 2018 at 1:35:44 PM UTC-5, Edward Prochak wrote:   
   > >   
   > > The solution is simple as long as the rules are applied correctly.   
   > > Words fail to reach the correct answer in your example.   
   > >   
   > > At start net angular momentum is zero L = I * w = 0   
   > > (Using w for omega, the angular speed)   
      
   > > So looking at just the person the angular momentum is initially   
   > >   Lp = Ip * wp   
   > >   
   > > Now holding the elastic band, you stretch your arms.   
   > > The momentum is conserved Lp = Ip' * wp'   
   > > but the rotational speed changed because of the change in the   
   > > moment of inertia (Ip).   
   > >   
   > > Now you lock the elastic band. You return your arms to their original   
   > > position, so we get to Lp = Ip" * wp"   
   > > Note this is double prime values, BECAUSE while the elastic band has   
   > > very little mass, it does contribute to the moment of inertia I.   
   > > So the final moment of inertia Ip" =/= Ip' and the rotational   
   > > speed is proportionally different also.   
   > >   
   > > So you conclusion is wrong. The momentum of the box + person   
   > > started at zero and remained at zero the entire process.   
   []   
   > You are over thinking. There is a short cut. You did not stretch the   
   > elastic band. Only the tendency of arms to spread out while spinning   
   > stretch the elastic band. Only energy from angular momentum stretched   
   > the elastic band not human power. With this in mind your short cut is   
   > energy was gained to stretch an elastic band. It did not come from the   
   > human energy so it had to come from angular momentum. As the the human   
   > was on a turn table when these actions took place the angular momentum   
   > of the box could not be effected. Therein is the rub. The equal angular   
   > momentum of the box and human on the turn table are no longer   
   > equal. Angular moment as not been conserved. The one on the turn table   
   > gave part of his angular momentum to stretch an elastic band. In effect   
   > nature was taken momentum in exchange for energy , stretched elastic   
   > band. As long as the elastic band remains stretched ENERGY conservation   
   > laws prevent restoration of angular momentum conservation between the   
   > box and the human on the turn table.   
      
   I did not specify the source of energy to stretch the band.   
   it could have been simply as you said.   
      
   The problem is that you are confusing angular speed and   
   angular momentum.  The angular speed is indeed different   
   after stretching the band, but the angular momentum of the   
   combined Person, elastic band, and turntable system remains   
   the same. This is because the moment of inertia changed also.   
      
   Linear inertia is due only to the total mass of the object.   
   The moment of inertia is dependent on the total mass and the   
   distribution of that mass (IOW, its shape).   
      
   So there is no rub which allows you to escape. It may be time   
   for you to do a little experimenting. Note that since you are   
   only dealing with the person, band and moving part of the   
   turntable, you can do the experiment at home.   
      
   But again I suggest that the "band" be something massive that   
   can make a more significant change in the moment of inertia.   
      
   It doesn't have to be elastic like a spring. A heavy weight   
   tied to two handles via pulleys. As you hold the handles   
   and widen your arms, it lifts the weight which is at the   
   center of the rotation. Make the handles something also heavy   
   (heavy enough to change the moment of inertia, but light   
   enough that even rotating, they can lift the heavy weight).   
      
   But also, you really need to look at the equations and work   
   a few examples, to see that there is no free energy here.   
      
   Enjoy,   
     ed   
      
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