Static equilibrium in physics 

In other words, for an object to be in static equilibrium, no net force or unbalanced external influence should act upon it to set it in motion.

Let’s consider a real-world example.

When we see a stationary object—like a cup resting on a table or a suspension bridge spanning a river—we often take for granted that it stays in place. It might seem as though nothing is happening.

However, behind this apparent simplicity lies a fundamental principle of physics: static equilibrium.

This concept is crucial for understanding everything from the stability of buildings and engineering structures to the way our own bodies maintain balance.

To analyze equilibrium conditions effectively, we distinguish between two types of objects: point masses and extended bodies.

• Point Mass
  An object can be treated as a point mass when its size is negligible compared to the physical phenomenon being studied (such as its motion). In this case, we focus solely on its position, ignoring its shape and dimensions. Generally, a point mass undergoes only translational motion.
  

  Example: In astronomy, a planet in orbit is often modeled as a point mass because its size is insignificant relative to the vast distances between celestial bodies.

• Extended Body
  An object is considered an extended body when its shape and dimensions affect its equilibrium behavior. In these cases, concepts such as the center of mass and torque become essential. Unlike point masses, extended bodies can undergo rotational motion in addition to translation.
  

  Example: A ladder leaning against a wall or a bridge beam requires an equilibrium analysis that accounts for weight distribution and the forces acting upon it.

Understanding the distinction between point masses and extended bodies allows us to analyze physical phenomena with greater precision.

Depending on the situation, we may model an object as either a point mass or an extended body.

Example: When striking a tennis ball with a racket, we must treat it as an extended body because the way it moves depends on its shape and the exact point of impact. By hitting it off-center, we can apply spin, causing it to rotate. However, once the ball is airborne, we can simplify our analysis by treating it as a point mass moving through space.

Conditions for Static Equilibrium

For a body to remain in static equilibrium, two fundamental conditions must be met:

• Translational Equilibrium
  The sum of all external forces acting on the object must be zero: \[ \sum \vec{F} = 0 \] This ensures that no net force is accelerating the object in any direction.
• Rotational Equilibrium
  The sum of all torques (moments of force) about any chosen point must also be zero: \[ \sum \vec{M} = 0 \] This prevents the object from rotating.

These two conditions govern the stability of every stationary object around us, from towering skyscrapers to everyday household items.

Static equilibrium is at play in countless aspects of daily life.

For instance, a four-legged table remains stable because gravitational forces and the normal forces exerted by the floor perfectly counterbalance each other. Another example is a person standing upright—our bodies constantly adjust the position of the center of mass to maintain balance.

Grasping these concepts is not only fundamental for physics students but also deepens our understanding of the physical world, from the mechanics of architecture to the way we stay on our feet.