The moment of inertia of a solid sphere (radius …, density 1)…

The moment of inertia of a solid sphere (radius $R$, density 1) adds up the hollow spheres of Problem 39: $I={\int }_0^{R}I(\rho )d\rho =$ ______. Divide by $m{R}^2$ (which is $\frac{4}{3}\pi R^5$) to find $J$ in the rolling experiment. A solid ball rolls faster than a hollow ball because ______.

This exercise builds on another exercise in its source book, which isn't shown here.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.4 Cylindrical and Spherical Coordinates, #40