1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted