if circle is a dimensional figure how can angular velocity and angular accelearation travel in the z direction of the 3 dimensional graph ?

 

The question is very good and deals with the vector analysis. It so happens is that the answer to this lies in tensor calculus which unfortunately is beyond the scope of syllabus here. However, to put it in simple terms, if a vector is dependent on two vectors then that vector has to take form in the direction perpendicular to the plane in which the two vectors are acting. So, angular velocity, angular acceleration and angular momenum all are directed along z-axis for a particle performing 2-D rotational motion.