The angular equation of motion of the pendulum is given by Newton's equation and with no external force it reads $$ \begin{equation} ml\frac{d^2\theta}{dt^2}+mgsin(\theta)=0, \tag{44} \end{equation} $$ with an angular velocity and acceleration given by $$ \begin{equation} v=l\frac{d\theta}{dt}, \tag{45} \end{equation} $$ and $$ \begin{equation} a=l\frac{d^2\theta}{dt^2}. \tag{46} \end{equation} $$