Skillful manipulation requires forming and recalling memories of the dynamics of objects linking applied force to motion. It has been assumed that such memories are associated with entire objects. However, we often control different locations on an object, and these locations may be associated with different dynamics. We have previously demonstrated that multiple memories can be formed when participants are explicitly instructed to control different visual points marked on an object. A key question is whether this novel finding generalizes to more natural situations in which control points are implicitly defined by the task. To answer this question, we used objects with no explicit control points and tasks designed to encourage the use of distinct implicit control points. Participants moved a handle, attached to a robotic interface, to control the position of a rectangular object ("eraser") in the horizontal plane. Participants were required to move the eraser straight ahead to wipe away a column of dots ("dust"), located to either the left or right. We found that participants adapted to opposing dynamics when linked to the left and right dust locations, even though the movements required for these two contexts were the same. Control conditions showed this learning could not be accounted for by contextual cues or the fact that the task goal required moving in a straight line. These results suggest that people naturally control different locations on manipulated objects depending on the task context and that doing so affords the formation of separate motor memories. NEW & NOTEWORTHY Skilled manipulation requires forming motor memories of object dynamics, which have been assumed to be associated with entire objects. However, we recently demonstrated that people can form multiple memories when explicitly instructed to control different visual points on an object. In this article we show that this novel finding generalizes to more natural situations in which control points are implicitly defined by the task.