Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_22

7/22 The vertical shaft and attached clevis rotate about the $z$-axis at the constant rate $\Omega = 4 \text{ rad/s}$. Simultaneously, the shaft $B$ revolves about its axis $OA$ at the constant rate $\omega_0 = 3 \text{ rad/s}$, and the angle $\gamma$ is decreasing at the constant rate of $\pi/4 \text{ rad/s}$. Determine the angular velocity $\vec{\omega}$ and the magnitude of the angular acceleration $\alpha$ of shaft $B$ when $\gamma = 30^\circ$. The $x$-$y$-$z$ axes are attached to the clevis and rotate with it.