Torque and rotational dynamics

The skill

Torque measures how effectively a force turns something: $\tau =rF\sin \theta$, where $r$ runs from the axis to the point where the force acts and $\theta$ is the angle between $r$ and the force. A force pointed along the radius makes no torque. Give each torque a sign for clockwise or counterclockwise; if they add to zero the system is in rotational equilibrium, and if not, $\alpha ={\tau }_{\text{net}}/I$. Rotational inertia, $I=\sum m{r}^2$, grows with the square of distance, so mass far from the axis matters most. A common error is measuring $r$ from the end of the object instead of from the axis.