I was looking at the idea that a hollow cylinder will have less velocity than a solid cylinder at the bottom of an incline.
I can find the velocity of the hollow and solid cylinder from the following:
PE = Translational KE + Rotational KE
From that equation I find v and I can see that v is greater for the solid cylinder.
So, I was thinking, what about two different thick walled cylindrical tubes? One tube less hollow than the other. Which would have the greater velocity and what would be the equation for velocity for each tube?
Starting again with PE = Translational KE + Rotational KE
so, mgh = 1/2mv² + 1/2 I ω²
Then the moment of inertia for a thick walled cylinder = 1/2m(r2² + r1²)
r2 being the radius of the whole cylinder
r1 being the radius of the inner hollow cylinder
Then ω = v/r (but which radius do I use???, I was thinking I should use r2, the radius of the whole cylinder)
The Attempt at a Solution
I would like a simple equation for v that includes r2 and r1 so I can see clearly how the velocity changes at the end of an incline if I had two different thick walled cylinders. I tried using the equations above, substituting into mgh = 1/2mv² + 1/2 I ω², but it's not working out for me. Any steps, guidance would be appreciated.