A cylinder of mass m is rotated about its axis by an angular velocity $\mathrm{\omega }$ and lowered gently on an inclined plane as shown in the figure. Then,

Frictional force f acting on the cylinder acts up the plane and f =$\mu$mg cos $\theta$=$\frac{1}{\sqrt{3}}mg \cos {30}^0=\frac{mg}{2}$

So net force acting on the cylinder = mg sin ${30}^0-f = 0$

 So, cylinder will remain in position till it stops rotating. After that, it will start rolling downwards.