How can I calculate the angular momentum of the Earth?

Question

13865 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-27T16:29:27

Follow the steps in the Explanation section.

Assume that the Earth is a uniform solid sphere. (This is not really true, but close enough.)
Use the formula for rotational inertia of a solid sphere rotating about a diameter: $I = \frac{2 \cdot M \cdot R^{2}}{5}$ $I = (2*M*R^2)/5$
Look up data of the Earth to use for M and R. Plug in the data to yield the rotational inertia in units of kg*m^2.
To calculate angular velocity, $ω$ $omega$ , you will use the fact that the Earth rotates thru $2 \cdot π$ $2*pi$ radians in 24 hours. Convert that time to seconds. Angular velocity, $ω$ $omega$ , is angular distance, in radians, divided by the time for that rotation -- the result will be in units of radians/s.
Use the formula $L = I \cdot ω$ $L = I*omega$ to find angular momentum in units of kg*m^2/s.

I hope this helps,
Steve