I came across this equation for balancing a pencil while solving some problems:
$$ml\ddot { \theta  } =mg\theta $$
Where $l=$the length of the pencil, and $\theta$ is the angle it makes with vertical. <br>
What I cannot understand is, why acceleration, $a=l\ddot { \theta  }$ and not $\displaystyle \frac { l\ddot { \theta  }  }{ 2 } $? <br> Is the center of mass located at its top and not the center? Or is there something else I am missing?