Translational and Rotational speeds

[hawk320]

Homework Statement

If a cylinder rolls down a 3.04 meter ramp with a 30 degree incline without slipping, how fast will the rotational and translational speeds be when the cylinder reaches the bottom of the ramp?

Homework Equations

mgh = K_rotational + K_translational
K_rotational = 1/2*I*omega^2
I_cylinder = 1/2*m*r^2
K_translational = 1/2*m*v^2
v= r*omega

The Attempt at a Solution

I can find out the translational speed by using the equation mgh = \frac{1}{2} * (\frac{1}{2} m r^2) \omega^2 + \frac{1}{2} m v^2
Which you can reduce down to mgh = 1.5 v^2 Since we know m,g and h we can solve for v.
But I can't seem to find a way to solve for omega without knowing the radius, when i reduce that equation down to solve for omega I always left with the radius somewhere. It may just be that you cannot solve for omega, but if you can find a way the help will be really appreciated.

 

[Shooting Star]

What if you put w=v/r?