Conservation of angular momentum with energy

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SUMMARY

The discussion centers on the conservation of angular momentum and its relationship with energy in the context of an ice skater's rotation. When the skater with moment of inertia I folds her arms, her moment of inertia decreases to I/2, resulting in a doubling of her rotational speed to W*2, thus conserving angular momentum. However, the energy calculation reveals that the rotational kinetic energy is not conserved; it doubles due to the work done by the skater in bringing her arms in, converting internal energy into rotational kinetic energy.

PREREQUISITES
  • Understanding of angular momentum and its formula (I*W)
  • Knowledge of rotational kinetic energy and its formula ((1/2)I*W*W)
  • Concept of moment of inertia and its impact on rotational motion
  • Basic principles of energy conservation and transformation
NEXT STEPS
  • Study the principles of angular momentum conservation in closed systems
  • Explore the relationship between rotational kinetic energy and work done
  • Learn about the effects of moment of inertia on rotational dynamics
  • Investigate real-world applications of angular momentum in sports and physics
USEFUL FOR

Physics students, educators, and anyone interested in understanding the dynamics of rotational motion and energy transformations in systems like ice skating.

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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