## Physics: Principles with Applications (7th Edition)

For a given mass and radius, the hoop has a moment of inertia more than twice that of a solid sphere. The kinetic energy is proportional to the moment of inertia, $KE = \frac{1}{2}I \omega^2$. Therefore the hoop has a greater initial kinetic energy and will ultimately rise farther up on the slope. (It turns out that the mass and size of the hoop and sphere don’t affect the final height. When using the conservation of energy equations in this problem, the mass and radius of the objects cancel out on both sides of the equation.)