Calculate the final angular velocity

Question

A cylinder with moment of inertia 12.9 kg m² rotates with angular velocity 2.03 rad/s on a frictionless vertical axle. A second cylinder, with moment of inertia 30.3 kg m², initially not rotating, drops onto the first cylinder and remains in contact. Since the surfaces are rough, the two eventually reach the same angular velocity. Calculate the final angular velocity.

Answer 1

Apply conservation of angular momentum, I₁ω_o + I₂ω_o = (I₁+I₂)ω

12.9(2.03) + 0 = (12.9 + 30.3)ω; ω = 0.606 rad/s