Consider the spinning disc shown in Figure 12.34, in which, a spinning conical shaft rises up into the opening in the center of the disc, and the disc begins to spin. Suppose the disc's rotational inertia is \(I_{\mathrm{d}}\), that of the shaft is \(I_{\mathrm{s}}\), and the shaft's initial rotational speed is \(\omega_{i}\). Does the rotational kinetic energy of the disc-shaft system remain constant in this process? Assume for simplicity that no external forces cause torques on the shaft.

Data from Figure 12.34