Centripetal acceleration of a point with velocity $v$ and moving on a path of radius of curvature $r$ is given by $v^2/r$. If $v= rw$ where $w$ is angular velocity of a body , then centripetal acceleration is given by $w^2r$.
So, my doubts are as follows:
Doubt 1: in pure rolling motion as velocity of lowermost point is zero so it’s centripetal acceleration should be equal to zero but it is traversing a path of radius of curvature r about the centre of object so it seems contradictory to me . Also, I was taught that acceleration of lowermost point is $w^2r$ and hence it has an acceleration towards the centre of the object which also confuses me.
Doubt 2 : Also, if the lowermost point has a centripetal acceleration and we solve any problem from the frame of reference of the lowermost point in a purely rolling object, then is a pseudo force $mw^2r$ applied on the centre of mass towards the lowermost point ? Or does the centre of mass have a centripetal acceleration towards the lowermost point that means a centrifugal force away from it?
Any help would be greatly appreciated!