# Angular Momentum conserved but not energy?

by say_cheese
Tags: skater problem
 P: 20 New to the forum- looked through the forum, but all are tangential answers. A skater with mass m, is spinning with arms extended to radius r1, with a tangential speed v1, angular velocity w1; v1=w1*r1, angular momentum mv1r1 =mw1r12; kinetic energy 1/2 m1v12. Now she pulls in her arms to a radius r2, r2r2, kinetic energy has increased by the square of (r1/r2). Where does this extra energy come from? (there should actually be an energy loss in the intermediate stage, where the skater is spiralling in to the new radius). Does the skater have to exert herself?
Mentor
P: 11,779
 Quote by say_cheese Does the skater have to exert herself?
Yes. Something similar is often done as a demonstration, with someone sitting on a freely rotating stool while holding weights in his outstretched hands. As he brings the weights in closer to his body, his angular velocity increases, and he has to make an effort to "pull the weights in", that is, he has to do work.
Mentor
P: 41,471
 Quote by say_cheese Since r1>r2, kinetic energy has increased by the square of (r1/r2). Where does this extra energy come from?
The skater must do work to bring her arms in. The extra energy comes from her converting chemical energy in her muscles into mechanical energy.
 Does the skater have to exert herself?
Exactly!

Mentor
P: 41,471
Angular Momentum conserved but not energy?

 Quote by say_cheese New to the forum- looked through the forum, but all are tangential answers.
This question pops up regularly, but our search function isn't so good. Here are two that I found:
http://www.physicsforums.com/showthr...88#post2610288

http://www.physicsforums.com/showthr...34#post1541734
 P: 20 Thanks guys/girls!
 P: 20 Thanks Guys/Girls!
 Sci Advisor Thanks PF Gold P: 12,170 There's always a 'Force timed Distance' somewhere to explain this sort of thing; it's a matter of spotting it. When you get down to it, it's that or The Twilight Zone.

 Related Discussions Beyond the Standard Model 10 Classical Physics 13 Introductory Physics Homework 9 Introductory Physics Homework 18 General Physics 9