9. [10] A star of mass M initially has a radius R; and an angular speed w;. Assume that there are no external torques on the star so that its

angular momentum must remain constant. This star is in the process of collapsing so that its radius becomes smaller but its mass remains the same. As a result of this contraction, at some point, the rotational inertia of the star become 1/3 of what is was initially. What has happened to star's rotational kinetic energy during this contraction? To answer this question, calculate a numerical value for the ratio of the star's kinetic energy after the contraction to its kinetic energy before the contraction.