# Torque question (qualitative)

1. The problem statement
what role does torque play in body stability and ergonomics ?

I'm not sure what level of explanation you want... Most simply, torque is a turning moment. The idea of torque is that if you apply a force at a greater distance, you get a bigger rotation - it would be easier to swing a cat by its tail than its middle (if you wished to swing cats), and it requires less effort to open a door from the edge, rather than at the pivot.

If you want a mathematical definition:

$$\tau_{Total} = \sum_{i} \tau_{i} = \sum_{i} \vec{r_{i}} \times \vec{F_{i}}$$

Where ##\tau_{Total}## is the total torque on the body, and is the sum of a number of torques, ##\tau_{i} = \vec{r_{i}} \times \vec{F_{i}}## where, ##\vec{r_{i}}## is the position vector, and ##\vec{F_{i}}## is the force.

The angular momentum of a body is related to the torque applied:

$$\vec{L} = \vec{r} \times \vec{p}$$

$$\frac{d\vec{L}}{dt} = \frac{d\vec{r}}{dt} \times \vec{p} + \vec{r} \times \frac{d\vec{p}}{dt}$$

So

$$\frac{d\vec{L}}{dt} = \vec{r} \times \vec{F}$$

i.e -if we don't have any torque, then the angular momentum must be constant in time. The body cannot be spinning up or spinning down - in cannot be changing its motion in any rotational sense. So in this way, we see that a necessary (but not sufficient! - e.g we also have to balance forces) condition for equilibrium is that the total torques on a body must be zero...

Does that help at all?

CWatters