Final answer:
Extending legs on a turntable increases moment of inertia, thus decreasing the rate of spin, due to the conservation of angular momentum.
Step-by-step explanation:
When the person on a turntable extends her legs while the turntable is being accelerated, the moment of inertia of the system increases. According to the conservation of angular momentum, when the moment of inertia (I) increases while the angular momentum (L) remains constant (since no external torques are acting), the rate of spin (angular velocity) must decrease. Formally, this principle is expressed as L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. When I increases due to the person extending their legs, ω must decrease to maintain the constant value of L.