I've been trying to solve this problem:
A cylinder is rolling down an inclined plane (angle between plane and horizon α). Coefficient of friction is µ. What is the translational and angular speed of the cylinder when it's traveled distance is l( at the beginning v = 0)? Assume that it rolls without slipping.
So basically I started with energy conservation:
$$
E_p=mgh=mgl \sin(\alpha)
$$
$$
E_p = E_r + E_t = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2
$$
$$
v^2 = 4gl \sin(\alpha)/3
$$
Now the tricky part is that we need to find angular speed, but we don't have the radius of cylinder... is there a way to find the radius? I was thinking of maybe momentum conservation law(though I don't understand it completely)?
Any help appreciated!