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Conservation of Angular Momentum for a Satellite

  1. Dec 19, 2015 #1
    1. The problem statement, all variables and given/known data
    https://scontent-sea1-1.xx.fbcdn.net/hphotos-xft1/v/t35.0-12/12414351_10206719685063143_386848762_o.jpg?oh=16c004481b7417fad921c37acc4942be&oe=56793416

    2. Relevant equations

    Angular momentum: H= Iw
    Parallel axis theorem: Io = I + Md^2
    Moment of Inertia of thin plate about it's center: (1/12)M(a^2+b^2)

    3. The attempt at a solution

    I calculated the initial moment of inertia of the satellite system by summing the moments of inertia for the four solar panels with the satellite.

    H(initial) = Inertia of satellite + 4 * Inertia of each solar panel
    = (0.940) + 4 [ (1/12) (20 kg) (0.75^2 + 0.2^2) + (20 kg) (0.575)^2 ]
    The moment of inertia was taken about the centroid of each solar panel and then parallel axis theorem was used to find the moment of inertia about the origin.

    H(final) = Inertia of satellite + 4 * Inertia of each solar panel
    = 0.940 + 4 [ (20 kg) (0.2)^2 ]
    The moment of inertia for the solar panels is considered to be the same as a point mass since it is vertical

    My questions are:
    a) Can we calculate the moment of inertia of a solar panel as if it's a point mass (post-rotation when it's vertical)?
    b) Where did the numbers from the solution come from?

    Thanks for taking the time to help
     
  2. jcsd
  3. Dec 20, 2015 #2

    SteamKing

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    Homework Helper

    It doesn't appear that the numbers in the 'solution' belong to this problem. I would ignore them.

    As far as the MOI of the panels when they are in the vertical position, the following diagram may help you calculate the MOI of each panel as it is rotating about an axis thru its length:

    mass-moment-thin-plate.jpg
    Of course, you would use the parallel axis theorem since the c.o.m.of each panel is displaced from the axis of rotation of the whole satellite.
     
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