Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_32

7/32 The small motor M is pivoted about the x-axis through O and gives its shaft OA a constant speed p rad/s in the direction shown relative to its housing. The entire unit is then set into rotation about the vertical Z-axis at the constant angular velocity \(\Omega\) rad/s. Simultaneously, the motor pivots about the x-axis at the constant rate \(\dot{\beta}\) for an interval of motion. Determine the angular acceleration \(\vec{\alpha}\) of the shaft OA in terms of \(\beta\). Express your result in terms of the unit vectors for the rotating x-y-z axes.