Question

How can I calculate the angular momentum of the Earth?

Answer 1

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 = (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.
3. To calculate angular velocity, `omega`, you will use the fact that the Earth rotates thru `2*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*omega` to find angular momentum in units of kg*m^2/s.

I hope this helps,
Steve