What is the Angular Momentum of the Earth Due to its Rotation?

[vpea]

I'm stuck on the second part of a problem and can't seem to get the right answer:

Calculate the magnitude of the angular momentum of the Earth due to its rotation around an axis through the north and south poles. Treat the Earth as a uniform sphere of radius 6.38*10^6 that makes one revolution in 24.0 hours. (m=5.97*10^24)

I got the answer 1.77*10^34 but it's wrong :(

 

[Doc Al]

Show your work. Explain how you got your answer.

 

[vpea]

I found the moment of Inertia (mr^2) to be = 2.43*10^38. Then found the angular velocity to be (2pi)/(24*60*60). Using the equation I=m*r^2, I got 1.77*10^34

 

[Doc Al]

Using the equation I=m*r^2...

That's the moment of inertial of a particle, not a solid sphere about its center. The one you want is $I = 2/5 m r^2$.

 

[vpea]

Thanks for that! I tried looking on the internet for the moment of Inertia of the Earth and was getting all sorts of weird numbers no wonder it wasn't working.

 

[jtbell]

I tried looking on the internet for the moment of Inertia of the earth

Every "General Physics" textbook I've ever seen has a table of formulas for moment of inertia of various shapes of objects. What kind of a course are you taking?