A disk, a hoop, and a sphere are released at the same time at the top of an inclined plane. They all roll?

Question

without slipping. In what order do they reach the bottom?

Answer 1

assuming they all have the same diameter and the same mass we start by calculating I, the moment of inertia, for each shape

Hoop: I = mr^2
Disk: I=mr^2/2
Sphere I=2mr^2/5 (assumes a solid sphere)

Without loss of generality, let m=1 and r=1

with have Hoop I=1
Disk I=1/2
Sphere I=2/5

The higher I the more reluctant the object is to rolling so the order of arrival should be Sphere, Disk, Hoop