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Homework Help: Angular momentum of a gyrocompass

  1. Dec 10, 2009 #1
    1. The problem statement, all variables and given/known data

    I have a gyrocompass with a fixed axis at an angle alfa to the rotational axis of the earth. Omega "Erde" is the angular momentum vector of the earth and Omega K is accordingly of the gyrocompass.
    The whole mass of the gyrocompass (m=0.1kg) is concentrated on the edge at a distance of R=1cm from the center of mass. The Gyrocompass is rotating with 10 000 RPM.

    I have to calculate the torque induced in the gyrocompass by the angle to the earth rotational axis.


    2. Relevant equations
    I guess that because of the form of the gyrocompass its moment of inertia should be I = m*r^2

    Angular momentum = I*omega
    Torque = I*omega'
    Omega K = 2*pi / T
    T (Period) = 60/10000

    3. The attempt at a solution

    I tried calculating the Omega Z component of the angular momentum of the gyrocompass with Cos(alfa)*Omega K, which I find via the moment of inertia and RPMs. Then I calculated the torque using only the Omega Z component, but that shouldn`t be correct, because the effect of the Earth angular moment isn`t taken into account and conservation of angular momentum, too.

    Any ideas would be greatly appreciated! By the way this is pretty urgent, I have to have it ready by tomorrow!
     

    Attached Files:

    Last edited: Dec 10, 2009
  2. jcsd
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