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.
What I cannot understand is, why acceleration, $a=l\ddot { \theta }$ and not $\displaystyle \frac { l\ddot { \theta } }{ 2 } $?
Is the center of mass located at its top and not the center? Or is there something else I am missing?