The angular momentum will remain constant when a spread out rotating body contracts since no external torque is applied but the KE of rotation is found to be changed what causes this change? Assume the case for a skater rotating about himself and contracting his arms.


marked as duplicate by Hritik Narayan, Yashas, sammy gerbil, John Rennie, David Hammen Jun 27 '17 at 12:16

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  • $\begingroup$ -1. Unclear. The force which causes the contraction supplies the work to increase KE. The source of this force is unknown. In the case of a skater, it comes from chemical energy. $\endgroup$ – sammy gerbil Jun 27 '17 at 10:58
  • $\begingroup$ @sammygerbil ok that explains it but what if the same force causes expansion then since the displacement of particles is in the direction of force work will be positive so how come the final KE comes out less than the initial. $\endgroup$ – user45838 Jun 27 '17 at 11:13
  • $\begingroup$ If the body expands, work must be done by the particles of the body eg to increase elastic energy stored in bonds or springs. So KE decreases and PE increases, which is opposite to what happens when the object contracts. $\endgroup$ – sammy gerbil Jun 27 '17 at 11:21
  • $\begingroup$ You don't need force from the arms to expand the rotating object. It will want to do that by itself so you just have to release whatever holds it back. $\endgroup$ – Steeven Jun 27 '17 at 11:45

If no torque is applied, there will be no change in the KE of the body. Just as there will be no increase in the KE of a non-rotating body if no force is pulling (or pushing) on it. The only thing happening is that rotating motion of all the parts of the body gets closer to the axis of rotation. For example, the outermost parts, having the highest velocity, take their velocity with them when the body contracts, so they travel the same distance per unit of time, but on a smaller circle, which means that their angular velocity (so not their instantaneous linear velocity) increases. They travel the same distance but need more turns to do so. This holds for all particles. So it is the angular velocity only that changes and not the KE present in the rotation.
The forces that pull the particles of the body inwards (or outwards) are perpendicular to the angular velocities so they cannot make them move faster (or slower).

  • 1
    $\begingroup$ This doesn't sound right, KE changes and momentum does not that is for certain, i am asking for what work changes the ke $\endgroup$ – user45838 Jun 27 '17 at 10:49
  • $\begingroup$ -1. If there is no torque, angular momentum does not change. Angular momentum of a particle is $mvr$. If $r$ decreases while $v$ remains the same the angular momentum is decreasing. You are correct in saying that there must be a force making the body contract, but wrong to conclude it has no influence on KE : eg chemical or elastic energy could be converted to KE. $\endgroup$ – sammy gerbil Jun 27 '17 at 10:52
  • $\begingroup$ @user45838-Of course I meant that the angular velocity only changes and not the angular momentum. I made a correction. $\endgroup$ – descheleschilder Jun 27 '17 at 11:14
  • $\begingroup$ @sammygerbil-What about a mass tied to the end of a rope turning around a thick round stick? The rope gets shorter, so the mass's velocity increases. Is the kinetic energy increased in this case? $\endgroup$ – descheleschilder Jun 29 '17 at 6:51

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