A rotating member for a wrap dispenser includes a first portion defining a first outer surface and a first inner surface, the first inner surface defining a first inner diameter; a second portion defining a second inner surface, the second inner surface defining a second inner diameter, wherein the first inner diameter is less than the second inner diameter; and an upset protruding radially outwardly from the first outer surface of the first portion, the upset oriented distal to the second portion, wherein a slot extends longitudinally through the upset to allow the upset to flex radially inward.