A rigid body is in static equilibrium when it remains at rest with no translational or rotational motion. This requires two conditions to be satisfied simultaneously: the net force must be zero, and the net torque about any point must be zero.

For a body in two dimensions, these conditions are expressed as:

The first two equations ensure translational equilibrium—the body does not accelerate linearly in any direction. The third equation ensures rotational equilibrium—the body does not begin to rotate. Together, these conditions guarantee that a stationary object remains stationary.

Common Forces

To apply these conditions, we must first identify all forces acting on the body.

Weight

Weight, or the gravitational force, $\vec{W} = \vec{F}_g= m\vec{g}$ of an extended object acts at the center of mass. For a shape with uniform mass distribution, the center of mass lies at the geometric center of the shape.

Normal Forces

Normal forces $\vec{N}$ act perpendicular to contact surfaces. Identify them by determining at which points two separate objects or surfaces make contact.

Note: Hinges often provide normal forces to secure one object to another. Normal forces from hinges can point in any direction since hinges are typically circular.