Moment of inertia of the earth

[nns91]

Hey guys,

I just calculated the moment of the inertia of the Earth using some data. I got the coefficient as 0.331, not 0.4 as for a solid sphere. What do you guys think it means ?

I reason the different of the 2 coefficient is because more mass of the Earth concentrates toward its center. But I don't understand how that contribute to the difference in moment of inertia. How would you guy explain this ?

 

[berkeman]

Hey guys,

I just calculated the moment of the inertia of the Earth using some data. I got the coefficient as 0.331, not 0.4 as for a solid sphere. What do you guys think it means ?

I reason the different of the 2 coefficient is because more mass of the Earth concentrates toward its center. But I don't understand how that contribute to the difference in moment of inertia. How would you guy explain this ?

From the definition of Moment of Inertia. Is this homework?

 

[nns91]

Nah, it's not my homework. How is this related to the definition of moment of inertia ?

 

[berkeman]

Nah, it's not my homework. How is this related to the definition of moment of inertia ?

You said in your first post above that you didn't understand why concentrating more mass at the center of the sphere would lower its moment of inertia, compared to a more uniform distribution. Write out the definition of the moment of inertia, and that should answer your question...

 

[nns91]

Moment of inertia is basically is the measurement of the resistance of an object to change in its rotation rate.

So what is the relationship here ?

 

[berkeman]

Show us the equation.

 

[A.T.]

I reason the different of the 2 coefficient is because more mass of the Earth concentrates toward its center. But I don't understand how that contribute to the difference in moment of inertia. How would you guy explain this ?

The closer the mass is to the rotation axis, the lower is its velocity and therefore momentum. So you need less momentum to make it spin.

 

[Bob S]

The moment of inertia of the Earth depends on its rotation rate (angular velocity) because the equatorial bulge of the oceans depends on the angular velocity. If the Earth's surface were 100% water, then the Earth's surface would be defined by a equipotential surface (oblate spheroid) (gravitational force - centrifugal force = constant). This might apply to the liquid core as well as the ocean surface.