You place a uniform solid disk and a uniform thin ring next to each other at the top of an incline of height h and release them from rest at the same instant.

$($a$)$

If they roll without slipping, what are the speeds of each when they reach the bottom? $($Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.$)$

vdisk$=$

$3\mathrm{.}62$

Can you apply conservation of energy? To what system? What types of kinetic energy are changing? How is the linear speed related to the rotational speed? What is the moment of inertia of a solid disk about its center of mass?vring$=$

$3\mathrm{.}13$h$$

The analysis is the same as for the disk, but what is the new moment of inertia?

$($b$)$

Which object reaches the bottom first?

solid diskthin ring$$It$\text{'}$s a tie.