Final answer:
To maintain the same angular velocity, the skaters can change the distribution of their masses while spinning. By shifting their positions, they can maintain the same angular momentum even if their angular velocities change.
Step-by-step explanation:
To have no change in angular velocity, the pair of figure skaters could change the distribution of their masses while spinning. By shifting their positions, they can maintain the same angular momentum even if their angular velocities change. For example, if the figure skater on the left moves closer to the axis of rotation and the figure skater on the right moves farther from the axis, their angular velocities can change but their total angular momentum would remain constant.