Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §14.4 Cylindrical and Spherical Coordinates, #39 · Multivariable Calculus · Change of variables

Find the moment of inertia around the … axis of a spherical…

Find the moment of inertia around the $z$ axis of a spherical shell (radius $ρ$ , density 1). The distance from the axis to a point on the shell is $r =$ ______. Substitute for $r$ to find
$I (ρ) = \int_{0}^{2 π} \int_{0}^{π} r^{2} ρ^{2} sin ϕ d ϕ d θ .$
Divide by $m r^{2}$ (which is $4 π ρ^{4}$ ) to compute the number $J$ for a hollow ball in the rolling experiment of Section 8.5.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.4 Cylindrical and Spherical Coordinates, #39

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