rotational kinetic energy and the stone has translational kinetic energy. Let mbe the mass of the stone and let Mbethe mass of the cylinder. For the cylinder The speed of the stone and the angular speed of the cylinderare related by Solve:Conservation of energy says and so The conservation ofenergy expression becomes so and9.43.Set Up:The speed of the weight is related to of the cylinder by where Usecoordinates where is upward and for the weight. where his the unknown distance the weightdescends. Let and For the cylinder Solve: (a)Conservation of energy says and (b)Reflect:The net work done by the rope that connects the cylinder and weight is zero. The speed of the weightequals the tangential speed at the outer surface of the cylinder, and this gives 9.44.Set Up:Ifor a point mass Ma distance Rfrom the axis is Solve: (a)For For a very short rod all the mass is at the axis.(b)For the same as for a slender rod with the axis through its center. The plate becomes a rodwhen its width gets very small.
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