4.0     INTRODUCTION

Definition of Equilibrium: An object is said to be in equilibrium when the net force acting on it is zero. This means that all the forces acting on the object balance each other out.

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TYPES OF EQUILIBRIUM

• Static Equilibrium: The object is at rest, and the sum of all forces and torques acting on it is zero.
• Dynamic Equilibrium: The object is moving at a constant velocity, and the sum of all forces and torques is still zero.

4.1     CONDITIONS FOR EQUILIBRIUM

• The sum of horizontal forces (ΣFx) must equal zero.
• The sum of vertical forces (ΣFy) must equal zero.
• The sum of moments (torques) about any point must equal zero (ΣM = 0).

4.2     TYPES OF FORCES

• Contact Forces: Forces that occur when objects are in contact (e.g., friction, tension).
• Non-contact Forces: Forces that act at a distance (e.g., gravitational force, magnetic force).

EXAMPLES OF EQUILIBRIUM 

• A book resting on a table is in static equilibrium because the gravitational force acting downwards is balanced by the normal force acting upwards.
• A car moving at a constant speed on a straight road is in dynamic equilibrium.

CENTER OF GRAVITY: The centre of gravity is the point at which the entire weight of an object can be considered to act. It is the average position of all the mass in the object.

          4.3     STABILITY

Stability refers to the ability of an object to return to its original position after being displaced.

TYPES OF STABILITY 

• Stable Equilibrium: The object returns to its original position after a slight displacement (e.g., a ball in a bowl).
• Unstable Equilibrium: The object moves away from its original position after a slight displacement (e.g., a ball on top of a hill).
  Neutral Equilibrium: The object remains in its new position after being displaced (e.g., a ball on a flat surface).

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FACTORS AFFECTING STABILITY

• The height of the centre of gravity: A lower centre of gravity generally increases stability.
• The base of support: A wider base increases stability.

CONDITIONS FOR EQUILIBRIUM OF RIGID BODIES UNDER THE ACTION OF PARALLEL FORCES

• The sum of vertical forces (ΣF) must equal zero.
• The sum of moments about any point must equal zero (ΣM = 0).

CONDITIONS FOR EQUILIBRIUM OF RIGID BODIES UNDER THE ACTION OF NON-PARALLEL FORCES

• The sum of forces in both horizontal and vertical directions equals zero.
• The sum of moments about any point equals zero.

4.4     EQUILIBRIUM OF COPLANAR FORCES

Coplanar Forces are forces that lie in the same plane. They can be resolved into components along the x and y axis.

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CONDITIONS FOR EQUILIBRIUM OF COPLANAR FORCES

• The sum of horizontal forces must equal zero ( ΣFx = 0 ).
• The sum of vertical forces must equal zero ( ΣFy = 0 ).

TRIANGULAR LAW OF FORCES: The triangular law of forces states that if three forces acting at a point can be represented in magnitude and direction by the three sides of a triangle taken in order, then the forces are in equilibrium.

PRINCIPLE OF MOMENTS: The Principle of Moments states that for an object to be in equilibrium, the sum of the clockwise moments about any point must equal the sum of the anticlockwise moments about that same point.

MOMENT OF A FORCE: The moment (or torque) of a force is defined as the product of the force and the perpendicular distance from the line of action of the force to the pivot point (moment arm).

Mathematically, it can be expressed as:

Moment (M) = Force (F) × Distance (d)

The SI unit of the moment is Newton-metre (Nm).

EQUILIBRIUM CONDITION OF MOMENT OF FORCE: For an object to be in rotational equilibrium, the following condition must be satisfied:

 Sum of Moment (clockwise) = Sum of Moment (anti clockwise).