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Side view R R/2 MM

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Question

A yo-yo is made of two uniform disks, each of mass M and radius R, which are glued to a smaller central axle of negligible mass and radius 0.5R (see figure). A string is wrapped tightly around the axle. The yo-yo is then released from rest and allowed to drop downwards, as the string unwinds without slipping from the central axle.

a) Find the moment of inertia, I, of the yo-yo with respect to an axis through the common centers of the disks, in terms of the mass and radius.

b) Calculate the magnitude of the linear velocity V, in meters per second, of the yo-yo after it has fallen a distance 0.46 m.

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