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Quiz (Rotation) - UC Berkeley Fall 2010 GSI Aaron Alpert...

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Physics 7A: Quiz 5 UC Berkeley, Fall 2010, GSI: Aaron Alpert Question 1. The rope shown in the figure is wound around a cylinder of mass 4 kg and ¯ I = . 02 kg · m 2 , about the cylinder’s axis. If the cylinder rolls without slipping, what is the linear acceleration of the center of mass? What is the frictional force? [Hint: Use an axis of rotation through the CM.] Question 2. Sarah is standing motionless on a turntable, holding a bicycle wheel horizontally directly over her head, as shown in the figure. The wheel’s an- gular velocity is 6 rad/s in the + k direction. Suddenly, Sarah twists the wheel so that now, the wheel’s CM is still directly over her head, but the wheel is vertical. In what direction, and at what speed, does Sarah rotate? Treat the bicycle wheel as a ring with mass 10 kg and radius . 3 m . Treat Sarah as a cylinder with mass 60 kg and radius . 25 m . For a ring I z = mR 2 and I x = 1 2 mR 2 , where I z is the moment of inertia about the central axis, and I x is the moment of inertia about a vertical axis. For a cylinder,
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