Solution
= Solution
The work law means that friction exerts a constant opposing <torque> of magnitude $W$. Until the cone stops,
$$
I\dot\omega=-W.
$$
Its initial angular speed is $\omega_0=\sqrt{2K_0/I}$, and uniform angular deceleration gives
$$
0=\omega_0-\frac WI t.
$$
Therefore
$$
\boxed{t=\frac{I\omega_0}{W}
=\sqrt{\frac{2K_0I}{W^2}}}.
$$