A disk with moment of inertia I₁ rotates about a frictionless, vertical a:de with angular speed ${\omega }_1$. A second disk, this one having moment of inertia l₂ and initially not rotating, drops onto the first disk (figure). Because of friction between the surfaces, the two eventually reach the same angular speed ${\omega }_f$ The value of ${\omega }_f$ is

A boy stands over the centre of a horizontal platform which is rotating freely with a speed of 2 revolutions/s about a vertical axis through the centre of the platform and straight up through the boy. He holds 2 kg masses in each of his hands close to his body. The. combined moment of inertia of the system is 1 kg$\times$metre². The boy now stretches his arms so as to hold the masses far from his body. In this situation, the moment of inertia of the system increases to 2kg$\times$metre². The kinetic energy of the system in the latter case as compared with that in the previous case will