# Vertical pendulum quick question

## Main Question or Discussion Point

hi pf!

i am looking at a simply problem dealing with an upside down vertical pendulum of length $L$ having mass $m$ at the top. i believe my professor wrote that a torque balance yields $m \ddot{\theta} = mg\sin \theta + f(t)$ where $f$ is a torque (i think) and $\theta$ is the angle the pendulum makes with the vertical axis.

my question is how the left hand side works? isn't newton's second law extrapolated for angular rotation as moment of inertia times angular acceleration equals sum of torques? if so, wouldn't we have $m L^2 \ddot{\theta} = mgL\sin \theta + f(t)$ as the torque balance?

## Answers and Replies

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BruceW
Homework Helper
hey, yeah, I think you're right. In any case, without the torque it should be
$$\ddot{\theta}=\frac{g}{L} \sin{\theta}$$
So maybe your professor forgot to write the $L$ in there.

edit: p.s. I'm guessing the angle is being measured from the highest point, hence no negative sign on the right hand side

thanks for your input! makes me feel better about it.