Answer
a) $\omega_f=1.09\times10^5\frac{rad}{s}$
b) $\omega_f=8.15\times10^4\frac{rad}{s}$
Work Step by Step
$I_i=I_f$
$I=\frac{2MR^2}{5}$
$\omega_i=\frac{1 rev}{9 days}\times\frac{2\pi rad}{1 rev}\times\frac{1 day}{86,400s}=8.08\times10^{-6}\frac{rad}{s}$
$\frac{2M_iR_i^2}{5}\omega_i=\frac{2M_fR_f^2}{5}\omega_f$
$\frac{2(8M_s)(6.96\times10^8m)^2}{5}(8.08\times10^{-6}\frac{rad}{s})=\frac{2(2M_s)(1.2\times10^4m)^2}{5}\omega_f$
$\omega_f=\frac{4(6.96\times10^8m)^2(8.08\times10^{-6}\frac{rad}{s})}{(1.2\times10^4m)^2}=108,724\frac{rad}{s}$
b) $108,724\frac{rad}{s}\times\frac{3}{4}=81,543\frac{rad}{s}$