# Calculate the magnitude of the angular momentum of the earth

1. Feb 4, 2010

### Chandasouk

1. The problem statement, all variables and given/known data

Calculate the magnitude of the angular momentum of the earth considered as a particle orbiting the sun. The mass of the earth is 5.97 x 10^24kg . Treat it as moving in a circular orbit of radius 1.50 x 10^11m at a speed of 2.98 x 10^4m/s

3. The attempt at a solution

I first try to find the moment of Inertia of the earth, I. I treated the earth as a solid sphere so

I=2/5(5.97 x 10^24kg)(1.50 x 10^11m)^2

= 5.373 x 10^46 kgm^2

I then found the angular velocity of the earth by

V=$$\omega$$r

2.98 x 10^4m/s/1.50 x 10^11m=$$\omega$$

$$\omega$$=0.000000199 rad/sec

Then

L=I$$\omega$$

L=1.069227 x 10^40 kg*m^2/s ?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 4, 2010

### rl.bhat

I first try to find the moment of inertia of the earth, I. I treated the earth as a solid sphere so
I=2/5(5.97 x 10^24kg)(1.50 x 10^11m)^2
= 5.373 x 10^46 kgm^2

It is wrong. Treat the earth as the particle
And in the above calculation you have substituted for R the radius of the orbit, not the radius of the earth.

3. Feb 4, 2010

### ehild

The problem asks the orbital angular momentum of the earth, as a point mass. The moment of inertia with respect to the centre of mass should be neglected.

By the way, you really think that the radius of Earth is 1.50 x 10^11 m ?

ehild