I understand that it can't be placed anywhere on the radius because it doesn't vary with it ( and so of course it doens't make sense to place it anywhere else on the plane), but why do we place it there?
I undertand all the advantages that came after $$\vec v = \vec\omega\times\vec r$$ $$\vec a = \vec\alpha\times\vec r + \vec\omega\times\vec v$$
but I can't see what's before.
PS. I know there is another question opened: Direction of angular velocity but I don't understand the answers given there (it's stated that angular velocity points in every direction of the circumference's plane!?) and I can't comment yet so please don't close this one. Thank you.