Equilibrium of a Particle Under Concurrent Forces

Physics · Laws Of Motion · NEET

A particle is in equilibrium when the net (resultant) of all forces acting on it is zero, so the particle stays at rest or keeps moving with constant velocity. For concurrent forces (all passing through one point), equilibrium means the vector sum is zero: this is checked by resolving into components, where the sum of x-components = 0 and the sum of y-components = 0. Memory hook: "Zero net force does NOT mean zero motion" — a body moving at constant velocity is also in equilibrium.
Equilibrium of a particle: three concurrent forces, net force = 0particleF1F2F3Same 3 forces head-to-tail close a triangleF1F2F3F1 + F2 + F3 = 0 (closed figure)
Left: free body diagram of a particle held by three concurrent forces. Right: the same three force vectors drawn head-to-tail form a closed triangle, showing their vector sum is zero — the condition for equilibrium.

Your doubts, answered

Does equilibrium mean the particle is at rest?

No. Equilibrium means net force = 0, so acceleration = 0. By Newton's first law, the particle either stays at rest OR moves with constant velocity in a straight line. Both are equilibrium. A skydiver falling at terminal velocity is in equilibrium even though moving fast, because weight balances air drag.

What does 'concurrent forces' mean?

Concurrent forces are forces whose lines of action all pass through one common point (the same particle). Because they act at one point, we only need to make the vector sum zero for equilibrium; we do NOT worry about torque or rotation (that comes with extended bodies later).

How do I check if a particle is in equilibrium?

Draw the free body diagram, choose x and y axes, and resolve every force into components. The particle is in equilibrium only if sum of x-components = 0 AND sum of y-components = 0 at the same time. If even one direction has a leftover force, there is acceleration and it is not equilibrium.

Why can three forces in equilibrium be drawn as a closed triangle?

If three concurrent forces add to zero, placing them head-to-tail as vectors brings you back to the start point — a closed triangle. NCERT states this directly: three forces in equilibrium can be represented by the sides of a triangle with arrows taken in the same sense. For n forces it becomes a closed polygon.

What is the difference between resultant and equilibrant?

The resultant is the single vector that replaces all the forces (their vector sum). The equilibrant is the single force equal in magnitude but opposite in direction to the resultant; adding it makes the total zero. In equilibrium the resultant is already zero, so no equilibrant is needed.

⚠️ The NEET trap
The particle is in equilibrium, so it must be at rest (velocity = 0).
Equilibrium only means net force = 0 and acceleration = 0. The velocity can be any constant value, including a large non-zero constant speed.
🧠 NTA loves the phrase 'moving with velocity V' and forces summing to zero — the answer is 'velocity remains constant', not 'stops'. Net force zero fixes acceleration, never speed.

Real NEET questions

2019

A particle moving with velocity V is acted upon by three forces represented by the sides of a triangle PQR (taken in order). The velocity of the particle will:

A · increase
B · decrease
C · remain constant
D · change according to the smallest force
Solution: Step 1: Three forces are represented by the sides of a triangle taken in order (head-to-tail), so they form a closed triangle. Step 2: Vectors forming a closed figure add up to zero, so the vector sum of the three forces = 0. Step 3: Net force = 0, therefore acceleration a = F/m = 0. Step 4: With zero acceleration the velocity cannot change, so the particle keeps moving with the same constant velocity V. This is Newton's first law / equilibrium of a particle. Correct answer: C (remain constant).

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Frequently asked

What is the condition for equilibrium of a particle?

The vector sum of all forces acting on the particle must be zero. In two dimensions this means sum of Fx = 0 and sum of Fy = 0 together, giving zero acceleration.

Is a body moving at constant velocity in equilibrium?

Yes. Constant velocity means zero acceleration, which means net force = 0. That is exactly the equilibrium condition, so uniform motion in a straight line is an equilibrium state.

What is the triangle law of equilibrium for three forces?

If three concurrent forces keep a particle in equilibrium, they can be drawn as the three sides of a triangle taken in the same sense (head-to-tail), because their vector sum is zero and the figure closes.

How many equations do we get for equilibrium in 2D?

Two independent scalar equations: sum of horizontal components = 0 and sum of vertical components = 0. These let you solve for two unknown forces or angles.

Why is equilibrium of a particle important for NEET?

Many Laws of Motion problems — strings, hanging masses, blocks on inclines, and connected bodies at rest — are solved by setting net force to zero. It is a fast, high-yield tool that avoids long calculations.