Definition: Equilibrium

Equilibrium – when an object has 0 net force and 0 net torque on it
Static Equilibrium – when in equilibrium while at rest (0 velocity and 0 angular velocity)

With these definitions in mind, the majority of Statics is problem solving using force and torque ideas. Here are a couple tips and ideas to keep in mind!

Theorem: Any Origin

If an object is in static equilibrium, the torque about any origin must be equal to 0.

Tip: Choosing an Origin

Often times, picking a good origin to take torque about can greatly simplify your work. a good point would be the intersection of the lines of many forces --- the torque from all those forces go to 0.

Idea: Virtual Work

We know that $F = -\frac{dU}{dx}$, so if $dU$ is $0$, then $F=0$, meaning equilibrium. Thus, if you consider a displacement of $dx$ to the system, and calculate the corresponding $dU$, we can solve the problem by setting $dU$ to $0$. A couple notes:

All possible displacements $dx$ must be considered
Best applied when a system is constrained and forces are complicated, but motion is not.

Idea: Friction + Normal Force Again

The sum of the friction force and normal force $\mathbf f = \mathbf F_f + \mathbf N$ points at an angle $\arctan \mu$ to the normal when the friction force is fully saturated.