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In the arrangement shown in Fig. 1.65 a weight A possesses mass m, a pulley B possesses mass M. Also known are the moment of inertia I of the pulley relative to its axis and the radii of the pulley R and 2R. The mass of the threads is negligible. Find the acceleration of the weight A after the system is set free.

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Let us depict the forces acting on the pulley and weight A, and indicate a positive direction for x and φ as shown in the figure. For the cylinder from the equation Fx=mg and 

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