Answer
See answers.
Work Step by Step
a. Treat the Earth as a uniform sphere. The angular frequency is $2 \pi$ radians per day.
$$KE=\frac{1}{2}I\omega^2=\frac{1}{2}\frac{2}{5}MR_{Earth}^2(\frac{2\pi rad}{86400s})^2=2.6\times10^{29}J$$
b. Treat the Earth as a point mass. The angular frequency is one revolution per year.
$$KE=\frac{1}{2}I\omega^2=\frac{1}{2}MR_{sun-Earth}^2(\frac{2\pi rad}{3.15\times10^7s})^2=2.7\times10^{33}J$$