Can $r$ just be the distance from an object center of mass to the axis of rotation?
If not, it will be very hard to calculate $r$ for things that are not particles, which doesn't exist in real life.
I am assuming that my book uses the distance from the center of the perfect sphere to to the axis of rotation. When the radius of rotation is small and close to the radius of the sphere, can you still take the distance from the center as $r$ and ignore the mass of other parts of the sphere?
Also does the position vector along $r$ have to perpendicular to the Angular acceleration vector?
So like if a problem just give you the acceleration which however is not tangent to the circular path of a rotating object, you have to ask for angle to find the component that is tangent to the path and perpendicular to $r$.