A circular disk of moment of inertia I_t is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed ω_i. Another disk…

A circular disk of moment of inertia $\displaystyle \mathrm{I}_{\mathrm{t}}$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\displaystyle \omega_i$. Another disk of moment of inertia $\displaystyle \mathrm{I}_{\mathrm{b}}$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $\displaystyle \omega_f$. The energy lost by the initially rotating disc to friction is :