Thanks! Reading this and pondering definitely helped me understand. > if we adopt the premise that the centripetal force is always perpendicular to the tangent

Thanks! Reading this and pondering definitely helped me understand. > if we adopt the premise that the centripetal force is always perpendicular to the tangential speed This also seems to be an extremely important element. I think the underlying thing that I wasn't getting was why the "pivot point" of the rotation moves the way it does.