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Physics help: rotational mechanics satellite

  1. Nov 21, 2007 #1
    1. The problem statement, all variables and given/known data
    A space station shaped like a giant wheel has a radius of 90 m and a moment of inertia of 4.50 108 kg·m2. A crew of 150 are living on the rim, and the station's rotation causes the crew to experience an acceleration of 1g (Fig. P10.47). When 100 people move to the center of the station for a union meeting, the angular speed changes. What acceleration is experienced by the managers remaining at the rim? Assume that the average mass of each inhabitant is 65.0 kg.

    2. Relevant equations

    3. The attempt at a solution
    I've tried a couple things, including finding the rotational momentum before and after the people move and setting them equal. I did take into account the different moments of inertia and solved for them with I + MR^2, with M being the mass of the people on the outside of the station. I don't know what I'm doing wrong.
  2. jcsd
  3. Nov 21, 2007 #2

    Doc Al

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    Staff: Mentor

    Everything you've described so far sounds correct. Show exactly what you did step by step and maybe we can spot an error.
  4. Nov 21, 2007 #3
    Okay, first I figured out the initial rotational velocity by using a=R(omega)^2, using 90m for R and 9.8 m/s^2 for a.
    Then I figured out the total initial moment of inertia by doing I + 150(M)(R)^2
    I used those to figure out the angular momentum by doing L=(I)(omega), using the I and omega I solved for above, not the given inertia.
    I then set rotational momentum equal to [I<sub>given</sub> + 50(M)(R)^2] x omega and solved for omega. Then I used that omega in a=M(omega)^2 to find total final acceleration.
  5. Nov 22, 2007 #4

    Doc Al

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    Staff: Mentor

    Looks great to me. That's how I'd do it. (Are you dealing with an online system? Sometimes they are picky as to the format of the answer.)

    What answers did you get for each step of your solution?
  6. Nov 22, 2007 #5
    Okay, I found my mistake. I just made an error adding the moments of inertia. Thanks for your help.
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