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There is something to be said in favor of picking the point of contact as the axis of rotation as far as simplification is concerned. One canOf course, usually you can simplify the task tremendously by choosing the body-fixed point and frame cleverly. For the orientation of the body-fixed basis it's of course very convenient to choose the principle axes of the tensor of inertia and, if the body is moving freely in space, the center of mass of the body as the body-fixed reference point.

__always__write the total kinetic energy as ## K = \frac{1}{2} I_P \omega^2 ## where ## I_P ## is the moment of inertia about the point of contact or axis of rotation. One can then use Steiner's (a.k.a. parallel axes) theorem to relate ## I_P ## to the moment of inertia about the center of mass. I adopted this point of view when I found out that students had difficulties "wrapping their head around" the dual concept of kinetic energy

**the center of mass and kinetic energy**

*of***the center of mass. My method sorts these terms out automatically.**

*about*Although I do not dispute what you are saying in general, I differ with you on this point. It is a mistake within the context of what I am trying to accomplish with this series of demonstrations. Before writing equations of motion for rolling objects, it is necessary for students to have a clear and fundamental understanding of what an axis of rotation is and how to find it. The purpose of the demonstrations is to do just that. Having this understanding is a precursor to describing the motion, whether it be in the lab frame or the CM frame. But OK, perhaps "wrong answer" in the original essay was a harsh label. "Misinformed answer" would have been more appropriate.That's why I don't think that you can call it a mistake choosing the body-fixed center of the disk as the reference point for the instantaneous angular velocity of the body as claimed in the article.