Motion of the wheel as it rolls up the fixed rack on its geared hub is controlled through the peripheral cable by the driving wheel D, which turns counterclockwise at the constant rate ω0 = 4.5 rad/s for a short interval of motion. By examining the geometry of a small (differential) rotation of line AOCB as it pivots momentarily about the contact point C, determine the magnitude of the angular velocity ω of the wheel and the magnitudes of the velocities of point A and the center O. Also find the magnitude of the acceleration of point C.