(b) On an old-fashioned rotating piano stool, a woman sits holding a pair of dumbbells at a distance of 0.60 m from the axis of rotation of the stool. She is given an angular velocity of 3.00 rad/s, after which she pulls the dumbbells in until they are only 0.20 m distant from the axis. The woman's moment of inertia about the axis of rotation is 5.00 kg-m² and may be considered constant. Each dumbbell has a mass of 5.00 kg and may be considered a point mass. Ignore friction. (a) What is the initial angular momentum of the system? (b) What is the angular velocity of the system after the dumbbells are pulled in toward the axis? (c) Compute the kinetic energy of the system before and after the dumbbells are pulled in. Account for the difference, if any

(c) A uniform rod has a moment of inertia for rotation around its long axis that is (1/2)MR². A cylindrical rod of uniform density is located with its center at the origin, and its axis along the z axis. Its radius is 0.03 m, its length is 0.5 m, and its mass is 2 kg. It makes one revolution every 0.03 seconds. If you stand on the +z axis and look toward the origin at the rod, the rod spins clockwise. What is the rotational angular momentum of the rod? Irot = kg · m2/s What is the rotational kinetic energy of the rod? Krot =

(II) A ball of mass M and radius r on the end of a thin massless rod is rotated in a horizontal circle of radius Ro about an axis of rotation AB, as shown in Fig. 10-58. (a) Considering the mass of the ball to be concentrated at its center of mass, calculate its moment of inertia about AB. (b) Using the parallel-axis theorem and considering the finite radius of the ball, calculate the moment of inertia of the ball about AB. (c) Calculate the percentage error intro- duced by the point mass approximation for r 1.0 m. s 9.0 cm and %3D Ro to Toinso odt 1s oizs IsB gadsion ai m %3D 08.2 (E 10-0 boT Ro UKE or da Problem 89. ► M 10-65 FIGURE 10-58 molecule. The H bonds incrtia Problem 58. A gl00A