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# SAexam4.soln - 212 Sample Exam 4 Do any three of the ff 4...

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212 Sample Exam # 4, ____________________ Do any three of the ff 4 problems: 1] A uniform square plate ( 2meter x 2meter; mass 6 kg) is pinned to the massless rod at O and is free to rotate around the z-axis. Find the angular acceleration α of the plate. I O α = Moment around O = Mg(meter / 2) = = 6 x 9.81 / 2 = 41.62 Nm I O = (I C =ML 2 / 6) + M d 2 where d = 1 meter = d OC I O = 6 2 2 / 6 + 6 1 2 = 10 kg m 2 So, α=4.16 rad / sec 2 2] The spool has a mass M and a radius of gyration of k. Cords are wrapped around inner and outer surfaces at r and R. One is attached to the ceiling, the other to a mass m. Neither cord slips. Find the acceleration of m. For full credit here it will suffice to find a set of purely algebraic eqns in a set of an equal number of unknown scalar quantities, and to indicate that this set suffices to solve the problem. T 2 R + T 1 r = Mk 2 α where Mk 2 is I cm of spo T 2 + Mg -T 1 = M a M mg - T 2 = ma m α r = a M α (R+r) = a m

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3] The S-shaped shaft consists of two half-rings, each of radius R=0.3meter and mass m/2 (m = 4kg).
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SAexam4.soln - 212 Sample Exam 4 Do any three of the ff 4...

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