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The cylinder of mass m is mounted on a gimbal that is free to rotate about the horizontal axis of shaft AB. As shown in the figure, the cylinder has a radius R and a length L. The cylinder is able to rotate about the axis through CD. The gimbal may be assumed to be massless. Initially, the cylinder is rotating at a constant rate about the axis through CD, but the gimbal is stationary. If a sudden impulsive torque t is applied to the gimbal along the shaft of AB for the generic angle shown, determine the angular velocity of the cylinder immediately after the impulsive moment. Express your answers in a body fixed coordinate system of the cylinder and in terms of variables like m,L,R, t,, and