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) + (1)/(2) I \omega^(2) = mgh + \frac{1}2} m r ^(2) \omega ^(2) + (1)/(2) I \omega^(2)`

for a solid cylinder:
`I = (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 = (mgh)/( \omega^(2) )`

That is as far as i get.