1.5.2 Turning Effect of Forces - Equilibrium

Objective

State that, when there is no resultant force and no resultant moment, an object is in equilibrium.

Key Concepts

An object is in equilibrium when it is not changing its state of motion. This means two conditions must be met:

• The resultant force acting on the object is zero.
• The resultant moment (or turning effect) acting on the object is zero.

Resultant Force

The resultant force is the vector sum of all the forces acting on an object. If the resultant force is zero, the object is not accelerating or decelerating.

Mathematically, if $\mathbf{F}$ is the resultant force, then $\mathbf{F} = 0$.

Resultant Moment (Turning Effect)

The resultant moment is the vector sum of the moments caused by all the forces acting on an object about a chosen pivot point. If the resultant moment is zero, the object is not rotating.

Mathematically, if $\mathbf{M}$ is the resultant moment, then $\mathbf{M} = 0$.

Equilibrium Condition

For an object to be in equilibrium, both the resultant force and the resultant moment must be zero. This can be expressed as:

$$ \text{Resultant Force} = 0 \\ \text{Resultant Moment} = 0 $$

Diagram

Applications

Understanding equilibrium is crucial in various real-world applications, such as:

• Designing stable structures (e.g., bridges, buildings).
• Analyzing the forces acting on objects in motion.
• Understanding the principles behind levers and other simple machines.

Condition	Result
Resultant Force = 0	Object is not accelerating or decelerating (translational equilibrium).
Resultant Moment = 0	Object is not rotating (rotational equilibrium).
Resultant Force = 0 and Resultant Moment = 0	Object is in equilibrium.