Final answer:
The fraction of the initial rotational kinetic energy that remains as rotational kinetic energy after the disks have come to their final common angular speed can be determined using the principle of conservation of angular momentum.
Step-by-step explanation:
The fraction of the initial rotational kinetic energy that remains as rotational kinetic energy after the disks have come to their final common angular speed can be determined using the principle of conservation of angular momentum.
The ratio of the final kinetic energy to the initial kinetic energy is given by the formula KE_final / KE_initial = I_finalω_final^2 / I_initialω_initial^2.
For example, if the disks have the same moment of inertia and come to the same final angular speed, then all of the initial rotational kinetic energy will be retained.