Conservation of angular momentum with energy

AI Thread Summary
The discussion centers on the conservation of angular momentum and its relationship with energy during a skater's arm movement. When the skater folds her arms, her moment of inertia decreases, causing her rotational speed to double, which conserves angular momentum. However, the energy increases due to the work done by the skater in pulling her arms in, converting internal energy into rotational kinetic energy. It is clarified that rotational kinetic energy is not conserved in this process. The key takeaway is that while angular momentum remains constant, energy can increase due to the work performed by the skater.
suhagsindur
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Ice sketar rotates with open arms & her moment of inertia is I, rotational speed W. So, angular momentum is I*W. Energy is (1/2)I*W*W
she folds her arms & her moment of inertia decreases to I/2. From conservation of angular momentum rotational speed became double say W*2.
Energy became (1/2)*I/2*W*W*4 = I*W*W ( Energy is doubled, How?)

Please tell me in this caculation where I am wrong?
 
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You're not wrong. The skater does work when she brings her arms in. She converts internal energy into rotational KE.
 
Rotational kinetic energy isn't conserved
 
OK, Very much Thanks for clearing my doubt.
 
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