# When a rotating body contracts what work causes the change in its rotational KE [duplicate]

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 HammenJun 27 '17 at 12:16

• -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. – sammy gerbil Jun 27 '17 at 10:58
• @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. – user45838 Jun 27 '17 at 11:13
• 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. – sammy gerbil Jun 27 '17 at 11:21
• 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. – Steeven Jun 27 '17 at 11:45

• -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. – sammy gerbil Jun 27 '17 at 10:52