Rotate, alternate can both mean to succeed or cause to succeed each other in turn.
Rotate may be used in reference to two or more persons or things; it implies indefinite repetition of the order of succession.
Thus, persons rotate in jobs or offices when they periodically interchange their jobs or offices according, usually, to a predetermined scheme; one rotates crops who grows different things on the same land in successive seasons in an order calculated to maintain soil fertility or to enrich exhausted soil.
Alternate differs from rotate in being referable only to two persons or things; though it also implies repetition of the order, it does not convey so strong a suggestion of continuity.