At the given instant, link $AB$ has angular velocity $2.9$ $rad/s$ and angular acceleration $5.4$ $rad/s^2$. Link $AB$ is $2.15$ $m$ long, link $BC$ is $0.78$ $m$ long and link $CD$ is $1.46$ $m$ long. Angle $\theta = 0.77$ $rad$ and angle $\beta = 0.9$ $rad$. Link $BC$ is horizontal at the instant shown. Determine the angular acceleration of link $CD$. (Hint: Solve for the angular velocities of link $BC$ and link $CD$ first, and then use them to solve for the angular acceleration of link $CD$).

$\alpha_{CD}=$ $rad/s^2$