TAM212SaExam4 - The shaft has total moment of inertia I zz...

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212 Sample Exam # 4, 15 October, 2004 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. 2] The above 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 equations in a set of an equal number of unknown scalar quantities, and to indicate that this set suffices to solve the problem. 3] The S-shaped shaft consists of two half-rings, each of radius R=0.3meter and mass m=2kg (total mass of shaft not counting straight sections = 4kg).
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Unformatted text preview: The shaft has total moment of inertia I zz = mR 2 /2 = 0.18 kg m 2 , and product of inertia I zy = 2R 2 m/3 π = 0.0764kg m 2 around x,y and z axes through point O. A constant torque (not pictured) of M z =0.20Nm k is applied to the shaft starting at time t=0. What is the angular speed ω after 4 seconds? What are the moments M x and M y on the shaft at time t=4 seconds? What are the forces Q x and Q y acting on the shaft at point Q at that time? Ignore gravity. 4] The uniform cylinder of radius R and mass m rolls to the right. It has a point mass (also m) attached as indicated on the rim. At the pictured instant the point mass is at the position indicated and the cylinder rolls with ω =1. Find the angular acceleration α of the cylinder....
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This note was uploaded on 05/24/2010 for the course TM 212 taught by Professor Richard during the Spring '10 term at University of Illinois, Urbana Champaign.

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