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# Statement of a problem № 3274

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The double pulley shown in Fig. 4.12 consists of two wheels which are fixed together and turn at the same rate on a frictionless axle. A rope connected to mass m1 is wound round the circumference of the larger wheel and a second rope connected to mass m2 is wound round the circumference of the smaller wheel. Both ropes are of negligible mass. The moment of inertia, I , of the double pulley is 38 kg m2 . The radii of the wheels are R1 = 1.2 m and R2 = 0.5 m. (a) If m1 = 25 kg, what should the value of m2 be so that there is no angular acceleration of the double pulley? (b) The mass m1 is now increased to 35 kg and the system released from rest. (i) For each mass, write down the relationship between its linear acceleration and the angular acceleration of the pulley. Which mass has the greater linear acceleration? (ii) Determine the angular acceleration of the double pulley and the te

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