Question

What is the moment of inertia of an object that rolls without slipping down a 2.00-m-high incline starting from rest, and has a final velocity of 6.00 m/s?

Answer 1

$E = mgh + \frac{1}2} m v^{2} + \frac{1}{2} I \omega^{2} = mgh + \frac{1}2} m r ^{2} \omega ^{2} + \frac{1}{2} I \omega^{2}$

for a solid cylinder:  $I = \frac{1}{2} m r^{2}$
for a hollow cylinder: $I = mr^{2}$

I will look at the case of a hollow cylinder:

$E = mgh + I \omega ^{2} = constant \\ \\ I = \frac{mgh}{ \omega^{2} }$

That is as far as i get.