Let's say a solid cylinder of radius r is rolling on a stationary horizontal surface with linear velocity v, angular velocity $\omega$, linear acceleration a and angular acceleration $\alpha$
Bottom most point is P
Now I require to find the acceleration of the point P (on the cylinder).
To do this first I could see it in the COM( Centre of Mass ) Frame. I observe it to have an $\omega ^2 r$ centripetal acceleration and a leftward $r\alpha$ tangential acceleration.
Coming to the ground frame I would have to add the acceleration of COM to it which cancels the $r\alpha$ component (as it is rolling) leaving $\omega ^2 r$ upward acceleration.
However I can't get the intuitive understanding as to why there exists a vertical component.
In the ground frame the velocity of P is 0 and so is the tangential acceleration. Due to no velocity I can't directly assume it to have a radial acceleration.
Could someone explain intuitively why it does? Or maybe how I could derive the same by completely solving it from the ground frame?