Calculating Earth's Angular Momentum: A Model of a Uniform Sphere

[Bashyboy]

The problem is:

"Model the Earth as a uniform sphere. Calculate the angular momentum of the Earth due to its spinning motion about its axis."

So, I first pointed out the the Earth rotates about its axis in 24 hrs x 3600 s / 1 hrs = 86400 s

Then I noted that a fixed point on the Earth rotates through a angle of 2pi, tracing out the circumference of the earth, in 86400s: $\omega=\frac{2\pi}{86400s}=7.27\cdot 10^{-5}$

The rotational inertia of the sphere being $I=2/3MR^2$

Angular momentum being $L=(2/3)(5.97\cdot 10^{24})(6.37\cdot 10^6)^2(7.27\cdot 10^{-5}=1.17\cdot 10^{34} kg\cdot m^2/s$ However, this answer is wrong. What did do wrong?

 

[SteamKing]

You've used the wrong moment of inertia. (Hint: is the Earth solid or hollow?)

 

[Bashyboy]

Hmm, it certainly isn't hollow. Thank you very much for the help.