In physics, the equilibrium of a particle refers to the state where the particle is either:

• At rest: The particle remains stationary in a specific location within its frame of reference.
• In uniform motion: The particle maintains a constant velocity (speed and direction) within its frame of reference. This means its speed isn’t changing, and it’s moving in a straight line.

Here’s a breakdown of the key points:

• Particle: In mechanics, a particle is considered a point-like object with mass. It has mass, but its size and shape are negligible for the specific problem being analyzed.
• Frame of reference: This is the frame we use to describe the motion of the particle. A common frame of reference is Earth’s surface, but it can be any reference point or coordinate system we choose.

Therefore, a particle is considered to be in equilibrium if there’s no net force acting on it, resulting in no change in its state of motion (either remaining at rest or maintaining constant velocity).

Here are some additional points to consider:

• Forces and Acceleration: When a net force acts on a particle that’s initially in equilibrium, it will cause the particle to accelerate. In other words, the particle’s state of motion will change.
• Equilibrium doesn’t imply absence of motion: As mentioned earlier, a particle in equilibrium can be moving with constant velocity. It’s the absence of acceleration (change in velocity) that defines equilibrium.

The concept of equilibrium is fundamental in various branches of mechanics, including:

• Statics: This branch deals with forces acting on stationary objects or objects in uniform motion. Analyzing equilibrium is crucial in statics problems.
• Dynamics: This branch studies the motion of objects under the influence of forces. Understanding equilibrium helps us analyze how forces cause changes in motion.