Question

Problem 7 A satellite consists two cylinders which can rotate relative to each other about the common axis of summetry. The rotation can be precisely controlled through a built-in motor. Both cyllinders can be asuumed to be uniform; they have the same mass, m 10.0 kg, and the same radius 0.30 m. The top cylinder has attached to it two balls, each of which has mass 1.0kg and radius b 0.1 m. Each ball is fastened to the end of a massless rod, and each rod sticks out of the cylinder perpendicularly to the axis of symmetry, each on the opposite side of the cylinder, so that the center of mass of each ball is a distance d away from the axis of symmetry The top cyllinder can adjust the two distances d using another built-in motor. The two blue dots are cameras, which both face in the same direction We want to reorient the satellite so that the cameras face in the opposite direction than they do now. This is done as follows: the distances d are extended each to 2.0m. The two cyllinders are rotated relative to each other at an angular velocity of 10.0 rpm for a certain number of seconds t1. The rotation is then stopped. The balls are then retracted so that they are touching the cylinder. The rotation is then started up again, but in the opposite direction, at the same speed, for t2 seconds. At the end, both cameras face in the direction opposite from that they were facing originally What do t and t2 have to be in order for this to work? What is the total angular distance traveled by the bottom cylinder? By the top cylinder? You will need the following result: Let ,CM be the moment of inertia of an object relative to an axis aCM that passes through its center of mass. Then the moment of inertia of the same object relative to an axis a that is parallel to acM is laacb M, where b is the distance between acM and a, and M is the mass of the object. (This is called the parallel axis theorem.) An example: in the book i is stated that the moment of inertia of a long uniform rod of length and mass m relative to an axis through its center is ICM- 2 m 12, while the moment of inertial of the same rod relative to an axis through its end is Ind-3m 1: here both axes are perpendicular to the length of the rod. The latter is a consequence of the parallel axes theorem: the distance between the axes is 1/2, so the parallel axis theorem says that I d ICM + (1/2)2 m =占me + ¼m 12, which is indeed me

Answer 1

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