As the author of this answer, I recommend you track the center of mass C with the equations of motion for rigid body and then find the end point motion at A and B.
Once the linear and angular acceleration of the center of mass $\vec{a}_C$ and $\vec{\alpha}$ is calculated then follow the formula for rigid body kinematics to get the acceleration at the end points.
For example for point A use:
$$ \begin{aligned}
\vec{v}_A & = \vec{v}_C+ \vec{\omega}\times(\vec{r}_A-\vec{r}_C) \\
\vec{a}_A & = \vec{a}_C + \vec{\alpha}\times(\vec{r}_A-\vec{r}_C) + \vec{\omega}\times(\vec{v}_A-\vec{v}_C)
\end{aligned} $$
Alternatively you can start from the end point velocities
$$ v_A = \dot{\theta} \ell \sin \theta \\ v_B = \dot{\theta} \ell \cos \theta $$
where $\theta$ is the rod angle from vertical and take the total derivative with respect to time to get the the accelerations at the end. To find the result you will need the angular speed and acceleration which you get from the rigid body equations of motion.