Moment of inertia of the earth

In summary, the conversation revolves around the calculation of the moment of inertia of the Earth and the discrepancy between the coefficient obtained and the expected value for a solid sphere. The reason for this difference is explained as the concentration of more mass towards the center of the Earth, resulting in a lower moment of inertia. The relationship between moment of inertia and the rotation rate of the Earth is also discussed, with the conclusion that the Earth's surface and liquid core may have different moments of inertia due to their varying densities.
  • #1
nns91
301
1
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 ?
 
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  • #2
nns91 said:
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?
 
  • #3
Nah, it's not my homework. How is this related to the definition of moment of inertia ?
 
  • #4
nns91 said:
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...
 
  • #5
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 ?
 
  • #6
Show us the equation.
 
  • #7
nns91 said:
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.
 
  • #8
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.
 

1. What is moment of inertia of the earth?

Moment of inertia of the earth refers to the measure of the earth's resistance to rotational motion around its axis. It is a property that is determined by the distribution of mass within the earth.

2. How is moment of inertia of the earth calculated?

The moment of inertia of the earth is calculated by considering the mass and distribution of the earth's mass. It is typically calculated using mathematical formulas and can vary depending on the shape and composition of the earth.

3. Why is moment of inertia of the earth important?

Moment of inertia is important because it affects the earth's rotation and overall stability. It also plays a role in determining the earth's shape and its gravitational effects on other objects in the universe.

4. How does the moment of inertia of the earth compare to other planets?

The moment of inertia of the earth is relatively small compared to other planets in our solar system. This is due to the earth's relatively small size and its relatively homogenous composition compared to other planets.

5. Can the moment of inertia of the earth change?

Yes, the moment of inertia of the earth can change over time due to various factors such as tectonic activity, changes in the earth's mass distribution, and external forces such as the gravitational pull of the moon and other planets.

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