Principle of Moments & Couples

What is the Principle of Moments?

The Principle of Moments states that for a body to be in equilibrium, the sum of the clockwise moments about a point must be equal to the sum of the anticlockwise moments about the same point.

In simpler terms, if you imagine a seesaw, it will balance if the turning effect (moment) on one side is equal to the turning effect on the other side.

The moment of a force is calculated using the formula:

$$\text{Moment} = \text{Force} \times \text{Distance}$$

Where:

• Force is measured in Newtons (N)
• Distance is the perpendicular distance from the pivot to the line of action of the force, measured in meters (m)

 

Understanding Couples

A couple is a pair of equal and opposite forces whose lines of action do not coincide. Couples produce rotation without translation.

The moment of a couple is given by:

$$\text{Moment of a couple} = \text{Force} \times \text{Perpendicular distance between the forces}$$

 

Conditions for Equilibrium

For a rigid body to be in equilibrium, the following conditions must be satisfied:

• The sum of all horizontal forces must be zero.
• The sum of all vertical forces must be zero.
• The sum of all moments about any point must be zero.

 

Example: Balancing a Beam

Consider a beam balanced at its center with weights on either side.

• If a 10 N weight is placed 2 m from the pivot on one side, and a 5 N weight is placed on the other side, how far from the pivot should the 5 N weight be placed to balance the beam?