How can I calculate the angular momentum of the Earth?
May 27, 2018
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 = (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,
#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.
- Use the formula
#L = I*omega#to find angular momentum in units of kg*m^2/s.
I hope this helps,