1. The problem statement, all variables and given/known data An Ice skater of mass m = 70kg is initially traveling at a speed v = 4 m/s along a straight path that brings his center of mass to within a distance b = .6m of a vertical pole fixed in the ice. He reaches out with his hand as he passes the pole and hangs on so that he pulls himself into a circular path of radius r = .8m (measured from the axis of rotation to his center of mass) around the pole. If the skater's moment of inertia about his center of mass is I = 1.40 kgm2 , what is his final angular velocity ω about the pole, assuming that no torques act during this maneuver? 2. Relevant equations Li = Lf Iiωi = Ifωf or maybe... L = mvr = Iω or possibly... mviri = mvfrf or if energy is conserved... .5mv2 = .5Iω2 I'm mostly confused about which formula to use. 3. The attempt at a solution mvri = Iω (70)(4)(.6) = (1.4)ω ω = 120 rad/s But I thought that this was a relatively unreasonable speed for the skater to be going, so I tried this... .5(70)(4)2 = .5(1.4)ω2 ω = 28.3 rad/s But I don't think energy is conserved, so I also tried this... mvr = mvr (70)(4)(.6) = (70)(v)(.8) v = 2.14 m/s v=ωr 3 = ω(.8) ω = 3.75 rad/s This seemed reasonable to me, but I didn't use the moment of inertia, and I have nothing to check my work against. How do I know which formula is the correct one to use in this situation?