3.54. Damn, Vorobiev

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3.54. A homogeneous thin rod length l = 1 m can freely rotate around a horizontal z axis passing through the point O on the rod. Rod turned down from its equilibrium position at an angle α and released (see. Fig. Below). Determine the angular velocity of the rod and the linear velocity of the point in the rod at the time of passage through the equilibrium position. The calculations are performed for the following cases: 1) a = 0, b = l / 2, α = π / 3; 2) a = l / 3, b = 2l / 3, α = π / 2; 3) a = l / 4, b = l, α = 2π / 3.

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