Moment of intertia

  1. Find the moment of inertia around the x-axis of the region that lies inside both the cylinder r=a and the sphere rho=2a.

    *Here's what I've done so far:

    Am I on the right track? If so, what's the next step? If not, what's wrong?
  2. jcsd
  3. quasar987

    quasar987 4,773
    Science Advisor
    Homework Helper
    Gold Member

    Well one mistake is that rho does not go from 0 to 2a. The cylinder is only of radius a.

    In any case, what I suggest is to break down the intergral into two parts. In the first, you'll integrate using cylindrical coordinates over the part of the cylinder enclosed in the sphere, and in the second, you'll integrate using spherical coordinates over the two little spherical caps of the cylinder. Be careful with the lower bound of the rho integral while integrating the spherical caps.
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