What you have done there is stating what is the basics of moment of inertia, and throwing nonsensical equations on the wall with vaguely defined terms and not explaining any of them.
“Perception”, in the case of yoyos is not as people says are impossible to analyze. It is quite apparent from basic physics principles to deduce that the perception of “fast” and “floatiness” of yoyos is entirely a result of a deviation between a player’s expectation and the actual physical properties of the yoyo. The real mystery here is how exactly is the player’s expectation influenced by the physical properties of the yoyo. The actual numerical relation can be quite complex to analyze, yes, but we can nail down the factors that influences by breaking down the question.
The first question we must ask ourselves, before going into any physics, is: is there any qualitative aspect of a yoyo that might influence the perception of the quantitative? Well, we have the shape, the finish, and the sound of the yoyo, which relates to comfort and, to a small degree, perception of the weight of the yoyo. Now, do any of these have lasting effects after the user is familiar with the design? The sound might gives the user an illusion of “hollow” or “solid”, and the shape may still contribute by affecting the rate in which the string slides down the catch zone. But from our experiences, these sensations are completely overshadowed by the our concentration on controlling the motion of the yoyo. Of course, some may experience the effect more than the others, but we can generally agree that when we focus our senses to the motion behavior of the yoyo it can be filtered out fairly effectively.
So we have concluded that the feel of the design in the hands of the user has minimum to negligible effect on the p