A neutron star is the compact remnant of a very large star that has exploded. Suppose that right after one such explosion, when much of the star's inertia has been blasted away, the star's remaining core has an inertia of \(4 \times 10^{30} \mathrm{~kg}\), a radius of \(13 \times 10^{8} \mathrm{~m}\), and completes one revolution every five days. What is the new spin rate once the core gravitationally collapses into a neutron star of radius \(20 \mathrm{~km}\) ? Assume negligible loss of inertia during the collapse.