Equilibrium

For an extended object to be in equilibrium, two conditions must be satisfied: Translational equilibrium $\sum \vec{F}=0$ Rotational equilibrium $\sum \vec{\tau }=0$

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 $\sum F_x=0$, $\sum F_y=0$, and $\sum M_P=0$

3D → We have 6 Independent Equations $\sum F_x=0$, $\sum F_y=0$ , $\sum F_z=0$ $\sum {\tau }_x=0$ , $\sum {\tau }_y=0$, $\sum {\tau }_z=0$

Principle of Transmissibility

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

Centre of Mass