What is the final rotational speed of the double rotating disks?

[Trentonx]

Homework Statement

A disk of mass M1 = 350 g and radius R1 = 10 cm rotates about its symmetry axis at f_initial = 152 rpm. A second disk of mass M2 = 258 g and radius R2 = 5 cm, initially not rotating, is dropped on top of the first. Frictional forces act to bring the two disks to a common rotational speed f_final.
a) What is f_final? Please give your answer in units of rpm, but do not enter the units

Homework Equations

T = I*a
I = (m*r²)/2

The Attempt at a Solution

I found the moment of inertia of M1
I = (.5)(.35)(.1²) = .00175 kg*m²
M2
I = (.5)(.258)(.05²) = .0003225 kg*m²
I found the angular velocity $$\omega$$
152rpm = 304pi rads/min = 5.06pi rads/sec
I don't suppose that I can just consider the mass to have just increased can I, because it specifies friction. I know some numbers, but how to put them together?

 

[Dr.D]

You know that energy is not conserved because friction is acting and heat is being generated. However, something else is being conserved. What is it?

 

[Trentonx]

L = I*w and L_i = L_f
Momentum would be conserved because the net torques act internally to the system. I get it, thanks for the hint.