(Solved): Consider two solid spheres with uniform mass distribution each: a small one with a radius R1 an ...

Consider two solid spheres with uniform mass distribution each: a small one with a radius $${\mathrm{R}}_1$$ and a large one with a radius of $$2?R_1$$. Initially the spheres are separated and rotate in the same direction about the same axis of rotation as shown below, the smaller sphere rotates with $${?}_1=27.9\mathrm{rad}/\sec$$ and the larger one with $${?}_2=2.3\mathrm{rad}/\sec$$, then the spheres are brought together. Friction acts between the spheres until both are eventually rotating at the same speed. Assuming that the spheres are made of the same material, what is the final angular velocity of the system? The final angular velocity of the system, $${?}_f=$$ Units How much energy is released as heat due to the friction if the mass of the small sphere is $${\mathrm{m}}_1=2.4\mathrm{kg}$$ and it's radius is $$R_1=0.85\mathrm{m}$$ ? The heat released, $$Q=$$ Units