Calculate the magnitude of the angular momentum of the earth

  • Thread starter Chandasouk
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  • #1
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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=[tex]\omega[/tex]r

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

[tex]\omega[/tex]=0.000000199 rad/sec

Then

L=I[tex]\omega[/tex]

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

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

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
rl.bhat
Homework Helper
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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
ehild
Homework Helper
15,543
1,914
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
 

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