Chapter 11, Problem 54P

A cylinder with rotational inertia $I_1=2.0 \text{kg}\cdot {\text{m}}^{\text{2}}$ rotates clockwise about a vertical axis through its center with angular speed ${\omega }_1\text{=5}\text{.0}\text{rad}/\text{s}$ . A second cylinder with rotational inertia $I_2=1.0 \text{kg}\cdot {\text{m}}^{\text{2}}$ rotates counterclockwise about the same axis with angular speed ${\omega }_2\text{=8}\text{.0}\text{rad}/\text{s}$ . If the cylinders couple so they have the same rotational axis what is the angular speed of the combination? What percentage of the original kinetic energy is lost to friction?