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
a)Find the total angular momentum of the skater and the masses both before and after the arm movement. Explain any difference
b) Find the total kinetic energy of the skater and the masses both before and after the arm movement. Explain any difference.
My attempt at part a) was that quite simply plug in the numbers into the equation L=Iw and gather the summation of the 3 objects however I assumed the arms of the skater were two rods with masses at the end and with axis of rotation at the end therefore meaning I use I = 1/3MR^2 however that is not the case, the answer simply uses I = MR^2 which confuses me.
My attempt at part b) was that K=1/2*I*w^2 but I am unable to generate a term of the kinetic energy before and after.
Any help on this would be greatly appreciated. Also any specific topics I could read up on to understand these concepts would be much appreciated.