An ice skater executes a spin about a vertical axis with her feet on a frictionless ice surface. In each hand she holds a small 5kg mass of which are both 1m from the rotation axis and the angular velocity of the skater is 10rad/s. The skater then moves her arms so that both masses are 0.5m from the rotation axis. The skaters own moment of intertia can be taken as being 50kgm^2, independent of her arm position.
Find the total kinetic energy of the skater and the masses both before and after the arm movement. Explain any difference.
KErotational = 1/2 Iω2
3. The Attempt at a Solution
KErotational initial = 1/2 Iω2 = 1/2 ((10⋅(1)2)+50)⋅(10)2
Then using the same method to find the final rotational KE once the skater has moved her arms in
KErotational initial = 1/2 Iω2 = 1/2 ((10⋅(0.5)2)+50)⋅(10)2
which doesn't make intuitive sense to me, since moving her arms in will increase her speed and should in turn increase her kinetic rotational energy?? on the worked answers for the exam they use the equation
where L is the angular momentum
can someone explain to me how the got that equation and why you cant use the other one, thanks.