When a star collapses it significantly shrinks in size and spins up$.$ Consider a star with a mass of M$=3\mathrm{.}651030$kg and an initial radius of Ri$=7105$km$.$ If the initial period of rotation of the star is Ti$=30\mathrm{.}1$days$,$ find the new rotational period after it collapses to a final radius of Rf$=7103$km$.$ Treat the star before and after the collapse as a solid sphere with uniform mass distribution $($which is not true, of course, but good enough for an estimation$).$