Calculate the magnitude of the angular momentum of the earth

[Chandasouk]

Homework Statement

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

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=\omegar

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

\omega=0.000000199 rad/sec

Then

L=I\omega

L=(5.373 x 10^46 kgm^2)(0.000000199 rad/sec)

L=1.069227 x 10^40 kg*m^2/s ?

 

[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.

 

[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