How can I calculate the angular momentum of the Earth?

1 Answer
May 27, 2018

Answer:

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