A horizontal turntable of rotational inertia \(I\) rotates freely about a vertical, frictionless axle with initial angular speed \(\omega_0\). A second, initially stationary disk of identical rotational inertia \(I\) is dropped gently and coaxially onto the turntable. Due to friction between their surfaces, the two disks slip against each other for a brief time before rotating together with a common final angular speed. Which of the following statements correctly relates the final rotational kinetic energy \(K_f\) of the two-disk system to its initial rotational kinetic energy \(K_i\) and provides the correct physical justification?