# How can I calculate the angular momentum of the Earth?

##### 1 Answer

May 27, 2018

#### Answer:

Follow the steps in the Explanation section.

#### Explanation:

- 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,

Steve