Finding acceleration using the instantaneous axis of rotation

Question

IAOR- instantaneous axis of rotation

Let's say a ball purely rolls on a horizontal surface

Normally the acceleration of the top most point will be $\omega ^2 R$ about the ball's center

But when finding acceleration using the concept of instantaneous axis of rotation it leads me to the wrong answer it will be $\omega ^2 2R$

But with instantaneous axis method the R term becomes 2R which is not the same as the original one

I do not run into such problems when finding velocity using IAOR .

Where have a fundamentally flawed ? Thanks alot in advance .

Please ask if anything is not clear

Answer 1

The normal acceleration of the top most point is $\omega^22R$ with respect to the Instantaneous axis of rotation but the axis itself accelerating upwards with $\omega^2R$ so the actual acceleration of the topmost is infact $\omega^2R$ wrt to the ground