A cylinder with moment of inertia I1 rotatesabout a vertical, frictionless axle with angular velocity i. A second cylinder; this one having amoment of inertia of I2 andinitially notrotating, drops onto the first cylinder. Because of frictionbetween the surfaces, the two eventually reach the same angularspeed f.(a) Calculate f. (Use I1 for I1, I2forI2, and omega_i for i, as necessary.)ωf= (b) Show that the kinetic energy of the system decreases in thisinteraction by calculating the ratio of the final to initialrotational energy. Express your answerin terms of ωi. (Useomega_i for ωi, I1 forI1, and I2for I2.)KEi= KEf= KEf /KEi=