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 $129kg*m^2.$ When one person is standing at a distance of $1\mathrm{.}56$ m from the center, the carousel has an angular velocity of $0\mathrm{.}609ra\frac{d}{s}.$ However, as this person moves inward to a point located $0\mathrm{.}731$ m from the center, the angular velocity increases to $0\mathrm{.}711ra\frac{d}{s}.$ What is the person's mass?