Draw a line from corner to corner on each 12-inch plywood sheet. The intersection of the lines is the center of the plywood. Draw a 12-inch diameter circle on one sheet and an 8-inch diameter circle on the second second sheet. Cut out the circles using your band saw. The 12-inch disk is the lower shelf to your rotating can rack and the 8-inch disk is the top shelf.
Drill a 1/4-inch deep hole in the centers of the disks and on the side with the lines. Insert the dowel into the hole on the 12-inch disc and screw through the plywood, into the dowel using one screw. Position your lazy Susan bearing over the 12-inch disk, opposite the side with the dowel -- so it is centered -- 2 inches away from the edges of the disk. Screw the bearing to the plywood in this position.
Insert the dowel into the 1/4-deep hole on the 8-inch disk. Screw through the disk and into the dowel using your last screw.