# The Rotational Kinetic Energy of the Earth

1. Nov 29, 2008

### soupastupid

1. The problem statement, all variables and given/known data

The Earth can be approximated as a sphere of uniform density, rotating on its axis once a day. The mass of the Earth is 5.97×10^24 kg, the radius of the Earth is 6.38×10^6 m, and the period of rotation for the Earth is 24.0 hrs.

What is the moment of inertia of the Earth? Use the uniform-sphere approximation described in the introduction.

I = (2/5)(5.97×10^24 kg)(6.38×10^6 m)^2
I = 9.720×10^37 kg m^2

why is it multiplied by (2/5) ?? is that value just given by a uniform sphere equation?

Consider the following statements, all of which are actually true, and select the one that best explains why the moment of inertia of the Earth is actually smaller than the moment of inertia you calculated.

A) The Earth is an oblate spheroid rather than a perfect sphere. For an oblate spheroid, the distance from the center to the equator is a little larger than the distance from the center to the poles. This is a similar shape to a beach ball resting on the ground, being pushed on from above.

B) The Earth does not have uniform density. As the planet formed, the densest materials sank to the center of the Earth. This created a dense iron core. Meanwhile, the lighter elements floated to the surface. The crust of the Earth is considerably less dense than the core.

C) While the Earth currently has a period of 24 hours, it is in fact slowing down. Once it was rotating much faster, giving days that were closer to 20 hours than 24 hours. In the future, it is expected that days will become longer.

2. Relevant equations

???

3. The attempt at a solution

The moment is lower because the mass is concentrated in the center in of the earth. It is not equally dense?

so its B right?

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2. Nov 29, 2008

### Staff: Mentor

Yes. An object's moment of inertia depends on how its mass is distributed--different shapes will have different moments of inertia. See: http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#cmi"
Good. The closer an object's mass is to the axis of rotation, the smaller its moment of inertia.

Last edited by a moderator: Apr 24, 2017