Assuming two hollow cyliders $C_{\text{in}}$ and $C_{\text{out}}$ with radius $r_{\text{in}}$ and $r_{\text{out}}$ such that $r_{\text{in}} < r_{\text{out}}$. Each of the cylinder is uniform and of length $L$. Now assuming $C_{\text{in}}$ is symmetrically placed inside $C_{\text{out}}$ without them touching. Both of them are rotating at $k$ rotations per second along x-axis in our reference frame in space. The x axis is their center of mass.
Does Conservation of Angular Momentum imply that no matter what physical/mechanical/chemical process these 2 cylinders try they would not be able to change their rotational speed from $k$ rpm to anything different.
We are asuming there is no 3rd object to change their angular momentum or apply torque or external force etc.