The small motor $M$ is pivoted about the $x$ -axis through $O$ and gives its shaft $O A$ 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 $\alpha$ of the shaft $O A$ in terms of $\beta .$ Express your result in terms of the unit vectors for the rotating $x$ -y-z axes.