Answer
a) $\omega_f=5.0\times10^{-2}\frac{rad}{s}$
b) $E_{Kf}=2.0\times10^4E_{Ki}$
Work Step by Step
a) $L_i=L_f$
$I_i\omega_i=I_f\omega_f$
$\omega_f=\frac{I_i\omega_i}{I_f}$
$\omega_f=\frac{\frac{2}{5}M_iR_i^2\omega_i}{\frac{2}{5}(0.5M_i)(0.01R_i)^2}=2.0\times10^4\omega_i\times\frac{2\pi}{30 days}\times\frac{1 day}{86400}=5.0\times10^{-2}\frac{rad}{s}$
b) $\frac{E_{Kf}}{E_{Ki}}=\frac{\frac{1}{2}I_f\omega_f^2}{\frac{1}{2}I_i\omega_i^2}=\frac{\frac{1}{2}\frac{2}{5}(0.5M_i)(0.01R_i)^2\omega_f^2}{\frac{1}{2}\frac{2}{5}M_iR_i^2\omega_i^2}$
$E_{Kf}=2.0\times10^4E_{Ki}$