# What is equilibrium

If the resultant of all the forces acting on a body is zero then the body is said to be in equilibrium.

# Static Equilibrium definition

If a body is in equilibrium, it will be either at rest or in uniform motion. If it is at rest, the equilibrium is called static equilibrium.

# Types of static equilibrium

Static equilibrium is of the following three types

1. Stable equilibrium
2. Unstable equilibrium
3. Neutral equilibrium

# Stable equilibrium definitions

If on a slight displacement from the equilibrium position, a body tends to regain its original position, it is said to be in stable equilibrium.

The equilibrium of a body is called stable If the body tries to regain its equilibrium position after being slightly displaced and released.

In stable equilibrium, the center of mass goes higher on being slightly displaced.

# Conditions for stable equilibrium:

For the stable equilibrium of a body, the following two conditions should be fulfilled.

1. The center of gravity of the body should be at the minimum height.
2. The vertical line passing through the center of gravity of the body should pass through the base of the body.

# Unstable equilibrium definition

If on slight displacement from the equilibrium position, a body moves in the direction of displacement and does not regain its original position, the equilibrium is said to be unstable equilibrium.

In this equilibrium, the center of gravity of the body is at the highest position.

The equilibrium of a body is called unstable if it gets further displaced after being slightly displaced and released.

In unstable equilibrium,the center of mass goes lower all being slightly displaced.

# Neutral equilibrium definition

If on slight displacement from equilibrium position a body does not tend to come back to its original position or to move in the direction of displacement, it is said to be in neutral equilibrium.

In neutral equilibrium, the center of gravity always remains at the same height.

If a body can stay in equilibrium even after being slightly displaced and released it is said to be in neutral equilibrium

In neutral equilibrium, the center of mass remains at the same height.

# Equilibrium conditions with example and formula

The center of mass of a body remains in equilibrium if the total external force acting on the body is zero. This follows from the equation F = Ma. Similarly, a body remains in rotational equilibrium if the total external torque acting on the body is zero. This follows from the equation ℸ = I𝜶.

Thus, if a body remains at rest in an inertial frame, the total external force acting on the body should be zero in any direction and the total external torque should be zero about any line.

We shall often find situations in which all the forces acting on a body lying in a single plane as shown in the given figure. Let us take this plane as the X - Y plane. For translational equilibrium

∑Fx = 0 ..........(i)

and

∑Fy = 0 .........(ii)

As all the forces are in the X - Y plane, Fz, is identically zero for each force and so ∑Fz = 0 is automatically satisfied.

Now consider rotational equilibrium. The torque of each force about the X-axis is identically zero because either the force intersects the axis or it is parallel to it. Similarly, the torque of each force about the Y-axis is identically zero. The torque about any line in the X - Y plane is zero.

Thus, the condition of rotational equilibrium is ∑ℸz = 0 ..........(iii)

While taking torque about the Z-axis, the origin can be chosen at any point in the plane of the forces. That is, the torque can be taken about any line perpendicular to the plane of the forces. In general, the torque is different about different lines but it can be shown that if the resultant force is zero, the total torque about any line perpendicular to the plane of the forces is equal. If it is zero about one such line, it will be zero about all such lines.

If a body is placed on a horizontal surface, the torque of the contact forces about the center of mass should be zero to maintain the equilibrium.

This may happen only if the vertical line through the center of mass cuts the base surface at a point within the contact area for the area bounded by the contact points. That is why a person leans in the opposite direction when he or she lifts a heavy load in one hand.