What nonlocomotor skill involves movement around an axis within a person's own space?

The nonlocomotor skill that involves movement around an axis within a person's own space is turning. This skill pertains to rotating the body around a central point or axis, such as the spine, allowing for various positions and orientations without necessarily traveling from one place to another. Turning is essential in many physical activities and sports, as it helps individuals change their direction while maintaining balance and control.

Bending and swaying are also nonlocomotor skills, but they primarily involve flexion and extension of body parts or shifting the weight from one side to another without a significant rotation around an axis. Kicking is distinctly a locomotor skill, as it typically involves moving a body part (the leg) to propel an object (like a ball) away. Thus, turning clearly stands out as the correct answer when focusing specifically on the rotation around an axis within one's own space.