A uniform solid star of mass \(M\) and initial radius \(R_0\) rotates about an axis through its center with initial angular velocity \(\omega_0\). The star undergoes core collapse to a final radius \(R_f\), during which its mass distribution shifts to a non-uniform density profile given by \(\rho(r) = \dfrac{C}{r}\) for \(0 \le r \le R_f\), where \(C\) is a constant. Assuming no external torques act on the star, what is the final angular velocity \(\omega_f\) of the star in terms of \(\omega_0\), \(R_0\), and \(R_f\)?