CONTEXT-RICH, ENGINEERING APPLICATION Figure 10-57 shows a

Chapter , Problem 76

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CONTEXT-RICH, ENGINEERING APPLICATION Figure 10-57 shows a hollow cylindrical tube that has a mass M, a length L, and a moment of inertia Inside the cylinder are two disks, each of mass m and radius r, separated by a distance , and tied to a central post by a thin string. The system can rotate about a vertical axis through the center of the cylinder. You are designing this cylinder disk apparatus to shut down the rotations by triggering an electronic shutoff signal (sent to the rotating motor) when the strings break as the disks hit the ends of the cylinder. During development, you notice that with the system rotating at some critical angular speed the string suddenly breaks. When the disks reach the ends of the cylinder, they stick. Obtain expressions for the final angular speed and the initial and final kinetic energies of the system. Assume that the inside walls of the cylinder are frictionless.