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Homework Help: Radius of Gyration Triple integral question

  1. May 18, 2010 #1
    1. The problem statement, all variables and given/known data

    By using spherical coordinates, find the radius of inertia (Is this the same as the radius of gyration?) about the z-axis of the constant density solid which lies above the upper half of the cone x2 + y2 = 3z2 and below the sphere x2 + y2 + (z-2)2 = 4. For a constant density region E of volume V, the radius of inertia about the z-axis is defined as:

    VR2 = ∫∫∫(x2 + y2)dV

    2. Relevant equations

    ρ2 = x2 + y2 + z2

    x = ρsin(φ)cos(θ)
    y = ρsin(φ)sin(θ)
    z = ρcos(φ)

    mR2 = I

    ...where R = radius of gyration and I = moment of inertia about a given axis.

    3. The attempt at a solution

    At this stage I am beyond confused. Any assistance in beginning this question would be greatly appreciated.
  2. jcsd
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