You sit at the middle of a large turntable at an amusement park as it begins to spin on nearly frictionless bearings, and then spins freely. When you crawl toward the edge of the turntable, does the rate of the rotation increase, decrease, or remain unchanged, and why

As there is no external torque is applied so the angular momentum remains constant.

L = I ω = constant

Where, I is the moment of inertia of the system and ω is the angular velocity

As we move towards the edge, the moment of inertia increases, hence the angular velocity decreases.