While you are beginning to learn about how objects rotate, it's worth taking an aside to discuss how objects remain still. You have already begin this work, when you read about Free Body Diagrams and worked with Young's Modulus. In both those cases, you read that an object at rest will remain at rest (it won't change its momentum) as long as the net force acting on the object is zero. It turns out that isn't the complete story. In these notes, you will read about static equilibrium, how the concept of torque plays a key role in defining static equilibrium, and how we analyze static equilibrium situations.

Forthcoming…

We define an object to be in static equilibrium if it is not moving. That seems obvious, but there's two specific conditions on the motion that have to be satisfied.

1. The object cannot be translating (moving up/down, left/right, etc.).
2. The object cannot be rotating (clockwise or counter-clockwise).

The first of these conditions you have dealt with previously when we discussed Free Body Diagrams. The first condition implies that the net force on the object must be zero:

$$\vec{F}_{net} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + \dots = 0$$

So if we analyze all the forces in each coordinate direction, they must sum to zero, for example,

$$\sum F_x = 0 \qquad \sum F_y = 0$$

If the sum of all the forces is zero then static equilibrium is possible but not guaranteed.

Consider the bar to the left 183_notes:statics_bar.png