Two discs with moments of inertia I rotate freely about the same vertical axis w

Question

Two discs with moments of inertia I rotate freely about the same vertical axis without friction. Initially one disc has angular speed omega_1 and the other omega_2 The discs come into contact and due to friction rotate together at the same angular velocity omega_f. What is the initial angular momentum? What is the final angular momentum? What is the final angular speed in terms of and omega_2? What is the initial kinetic energy of the system of both discs? Write an expression for the ratio of the final kinetic energy to the initial kinetic energy. Your answer should be in terms of omega_1.omega_2, and I. Find the numerical value of this ratio of kinetic energies in the case where I = 2 kg m^2, omega_1 = 6 radians/s, and omega_2 = 3 radians/s. Correct answers have correct units.

Explanation / Answer

1] Initial angular momentum,Li= Idisc[ w1+w2] { Idisc= mr2/2 , where r is the radius of the disc}.

2] Final angular momentum,Lf= I'discwf   { I'disc= mr2/2 + mr2/2 = mr2 , where r is the radius of the disc}.

3] Initial kinetic energy ,KEi= 1/2*Idisc[ w12+w22]

4] Final kinetic energy ,KEf= 1/2*I'disc* wf2

Ratio-------- KEf / KEi= wf2 / [ w12+w22]

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