Answer
The thin-walled hoop stores the most energy, and the rotating rod stores the least.
Work Step by Step
Using Table 9.2, the moments of inertia of the 4 objects are:
$\frac{1}{10}MD^2$ for the solid sphere
$\frac{1}{8}MD^2$ for the solid cylinder
$\frac{1}{4}MD^2$ for the thin-walled hoop
$\frac{1}{12}MD^2$ for the rod
The kinetic energy is $\frac{1}{2}I\omega^2$.
The thin-walled hoop has the largest moment of inertia, and the rotating rod has the smallest.
