Limits on the comprehension of rotational motion: mental imagery of rotations with oblique components

Mental imagery of rotational motion across variation in the orientation of a square to an axis of rotation, the orientation of the axis to the environment/viewer, and the starting orientation of the rotation were investigated in three experiments. The experimental method included specifying the particular rotations that subjects should consider and obtaining exact predictions of the outcomes of the rotations. When the square was normal to the axis and the axis was normal to the environment/viewer, performance was excellent. When either of these relationships was oblique, performance was quite good. When both of these relationships were oblique, nearly every subject made large errors on every problem. The difficulty of the double-oblique rotations was reduced when the initial orientation of the square was not canonical. Current views of the comprehension of rotational motion are discussed. It appears that the comprehension of rotational motion can be understood as an organizaiton of the symmetric space traced out by the motion. People succeed in organizing this space when it is aligned with a principal spatial reference system.