The moment of inertia of a uniform sphere is NOT (1/2) M R^2. Try that part again.
http://scienceworld.wolfram.com/physics/MomentofInertiaSphere.html
What you want to calculate is
Rotational KE = (1/2) I w^2
w is the angular velocity for ROTATION in radians per second, and equals 2 pi divided by the number of seconds in a sidereal day (23 hours, 56 minutes)
The circular path assumption does NOT have to be made. They are either trying to confuse you or the teacher who assigned the question is not well trained.
(a) Calculate the kinetic energy that the earth has because of its rotation about its own axis. Assume that the earth is a uniform sphere and that its path around the sun is circular. For comparison, the total energy used in the United States in one year is about 9.33e9 Joules.
I found moment of inertia by .5xMRe2
How do you find angular velocity?
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