How can I calculate the angular momentum of the Earth?

May 27, 2018

Follow the steps in the Explanation section.

Explanation:

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

I hope this helps,
Steve