A hard disk drive (HDD) has a stack of disks mounted on a rotatable spindle with the disks being movable axially, i.e., in a direction parallel to the axis of rotation of the spindle. A disk separator is located inside the spindle and separates axially-adjacent disks in a pair to create an axial gap. Any pair of axially-adjacent disks can be separated so that different axial gaps are created. A single head-arm assembly with at least one and preferably two read write heads is movable axially so that it can be rotated by the rotary actuator into any one of the axial gaps. The read/write heads can thus access data on the disk surfaces in the axial gaps. When it is desired to have the disk separator create an new axial gap and thus a new pair of disk surfaces to be accessed, the actuator rotates the head-arm assembly away from the outer perimeters of the disks and moves the read/write heads onto a head support structure that supports the read/write heads off the disks.