Do cylinders with equal rotational energy have the same tangential velocity?

[hatephysics]

Homework Statement

If two cylinders have the same rotational energy, do the cylinders, though having either different radii or different masses, have the same tangential velocity?

Homework Equations

Rotation Equations (torque, etc)

The Attempt at a Solution

My gut feeling says yes, because of the conservation of energy.

Thank You for any help.

EDIT: My gut feeling says yes, because of the conservation of angular momentum?

 

[ideasrule]

If you have two identically-shaped cylinders rotating at the same speed, one made out of snow and the other made out of lead, which will have a greater rotational kinetic energy?

 

[hatephysics]

If you have two identically-shaped cylinders rotating at the same speed, one made out of snow and the other made out of lead, which will have a greater rotational kinetic energy?

I guess the lead one would because of the greater inertia, but what about the case with different radii. The way I see it is, they both follow .5I(omega)^2 so the larger cylinder will have a larger radius but a small angular velocity. But, tangential velocity is multiplying both radius and angular velocity so won't the tangential velocity be equal in this case?

 

[hatephysics]

Well, I tried using an arbitrary case and my new answer is "no" but I still don't quite get why.
In my case, I designated the radius to be multiplied by 4 and the angular momentum to be multiplied by .5

 

[ideasrule]

0.5Iw^2 can be rewritten as 0.5I(v/r)^2. Since I=(1/2)Mr^2 for a cylinder, KE=(1/4)Mv^2. So radius doesn't affect kinetic energy as long as mass is constant.