In a very real sense, there is nothing new about rotational motion.  How objects rotate about an axis works in exactly the same way as how the center of mass of an object moves through space.  The relationships between displacement, velocity, and acceleration are the same.  It is just that they hold for the rotational versions of those variables as much as they do for the translational versions.  If anything, describing the rotational motion of an object about an axis is even easier than describing how an object moves because we will choose to limit ourselves to rotations about a single axis.  Just like we chose to keep things relatively simple by limiting the translational motion of an object to two dimensions, we will only worry about how an extended object rotates about one axis.  As a result, we are limiting ourselves to one-dimensional vector problems to describe an object’s rotation, and just need to keep track of the signs of our variables once we have picked a coordinate system to break vectors up into their components.