Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 139 kg-mz. When one person is standing at a distance of 1.47 m from the center, the carousel has an angular velocity of 0.650 rad/s. However, as this person moves inward to a point located 0.509 m from the center, the angular velocity increases to 0.790 rad/s. What is the person's mass