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Homework Help: Calculate the magnitude of the angular momentum of the earth

  1. Feb 4, 2010 #1
    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=[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 ?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 4, 2010 #2

    rl.bhat

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    Homework Helper

    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.
     
  4. Feb 4, 2010 #3

    ehild

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    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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