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, r2<r1. Angular momentum is conserved. She changes her tangential speed to v2 and angular velocity to w2. so mv1r1=mv2r2 or v2 = (v1*r1)/r2 But the new kinetic energy 1/2mv22= 1/2mv12*(r1/r2)2 Since r1>r2, 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?