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Physics 121B, Autumn Quarter 2013 Honors Physics Homework Assignment 5 Due 9:30am Wednesday October 30 1. A sphere rolls up an inclined plane of inclination angle 30. At the bottom of the incline the center of mass of the sphere has a translational speed of 16 m/s. (a) How far does the sphere travel up the plane? (b) How long does it take to return to the bottom? 2. A circular turntable rotates at constant angular velocity about a vertical axis. There’s no friction and no driving torque. A circular pan rests on the turntable and rotates with it. The pan is covered with a layer of ice of uniform thickness, which is, of course, also rotating with the pan. The ice then melts and none of the water escapes from the pan. Is the angular velocity now greater than, the same as, or less than the original angular velocity? Justify your answer. 3. A uniform disk of mass M and radius R rotates about a horizontal axis with angular speed . (a) What’s its kinetic energy? (b) What’s its angular momentum? (c) A chip of mass m breaks off the edge of the disk at an instant such that the chip rises vertically above the point at which it broke off. How high above the breaking-point does it rise before starting to fall? (d) What’s the final angular speed of the broken disk? (e) What’s the final angular momentum of the broken disk? (f) What’s the final energy of the broken disk? (This problem will be graded. Ensure you neatly tabulate your answers to ease the grader’s task. Sloppy and untabulated work will be downgraded.) 4. Moore unit C problem C14S.5 (cat and turntable). [ver 23oct13 17:20]