Zorro swings from a small chandelier, which is supported by 5 vertical chains, e

Question

Zorro swings from a small chandelier, which is supported by 5 vertical chains, each of length 3.2 m. The tension T in each chain reaches a maximum of 257 N, at the chandelier's lowest point, when Zorro's center of mass is 1 m directly below the chandelier. What is the combined angular speed, w (in rad/s), of the chains, Zorro, and the chandelier at this moment, measured with respect to the point on the ceiling where the 5 chains are attached? The chandelier weighs 106 N, while Zorro weighs 937 N. Neglect the weight of the chains.

Explanation / Answer

center of mass = 106*3.2+937*4.2/(106+937) = 4.09837009 m; effective weight = (106+937) = 1043 N; (1043/9.8)*4.09837009*w^2 = 1285 - 1043 = 242 N; w = sqrt(242/436.183674) = 0.744857131 rad/sec angular velocity (entire system) = 0.744857131 rad/sec

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