# Equilibrium

For an extended object to be in equilibrium, two conditions must be satisfied:
**Translational equilibrium**
$∑F=0$
**Rotational equilibrium**
$∑τ=0$

### Static vs Dynamic Equilibrium

Static equilibrium: No linear motion and no rotational motion

Dynamic equilibrium: Constant linear velocity and/or constant angular velocity.

### Stable, Unstable, and Neutral equilibrium

**Stable equilibrium**: the object tends to return to its equilibrium position.

**Unstable equilibrium**: a small displacement will cause the object to move away from its original position.

**Neutral equilibrium**: when we displace this object, it will simply remain in the new position.

## Scalar Form

2D → We have 3 Independent Equations $∑F_{x}=0$, $∑F_{y}=0$, and $∑M_{P}=0$

3D → We have 6 Independent Equations $∑F_{x}=0$, $∑F_{y}=0$ , $∑F_{z}=0$ $∑τ_{x}=0$ , $∑τ_{y}=0$, $∑τ_{z}=0$

If there is static equilibrium, then for any arbitrary point A we choose its moment is also 0.