A mechanism composed of a vertical axis that rotates, supported by fixed bearings, with angular velocity α& . At a point “O” of this vertical axis, a rod that rotates with angular velocity β and with respect to the vertical axis is fixedly pivoted. On this second rod is mounted a disk of radius r whose CG is denoted by the point “G”. The disk, in addition to rotating with respect to the rod with angular elocity θ , has a translational movement with respect to the rod. The position of the CG of the disk with respect to the pivot point “O” of the rod is defined as a distance L. Determine:

i) The absolute position vector of any point “A” on the periphery of the disk described in the inertial reference system;
ii) From the result found in item (i), the absolute linear velocity of point “A” obtained directly from the inertial reference system;
iii) The absolute angular velocity of the disk;
iv) The absolute angular acceleration of the disk;
v) The absolute linear acceleration of point “A” obtained directly from any mobile reference system;