Moment of a Force

Turning force (moment of a force)

A turning force, also known as a moment of a force, is the measure of the ability of a force to rotate an object about a fixed point (pivot or fulcrum).

Effect of a turning force

When a force is applied to a body that can rotate around a fixed point (pivot), the effect of the force depends on:

1. The magnitude of the force.
2. The distance from the point of application of the force to the pivot.

If the conditions allow, the body will:

1. Rotate in the direction of the applied force,
2. Stop if previously rotating in the opposite direction,
3. Or remain balanced if the moments are equal on both sides of the pivot.

Moment of a force (turning effect)

The moment of a force about a point is the product of the force and the perpendicular distance from the pivot to the line of action of the force.

$$\text{Moment} = \text{Force} \times \text{Perpendicular Distance from Pivot}$$

Unit: The S.I unit is Newton meter (Nm).

Examples of turning forces

1. Opening a door (the handle is far from the hinges to increase the moment).
2. Using a spanner to turn a bolt.
3. Balancing a see-saw.

The Moment of Force

The moment of force about a point is the turning effect of the force about that point. The change in the state of a body can appear in several forms, and the most common form is the turning effect, referred to as the moment of force.

When undoing a nut fastened to a screw by hand, one realizes that the amount of force required is much greater than when undoing the same nut using a spanner. The spanner increases the distance between the fulcrum and the line of action of the force. Thus, for the same force, a greater moment is obtained.

The unit for force is Newton (N), while the unit for the moment of force is Newton-meter (Nm).

Formula for Moment of Force:

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

Or, more succinctly:

$$\text{Moment} = F \times x$$

Consider the diagram below;

Moment of W₁ about the fulcrum. = W₁d₁

Moment of W₂ about fulcrum = W₂d₂

The Principle of Moments

The Principle of Moments states that: "If a body is in equilibrium under forces that lie in one plane, the sum of the clockwise moments is equal to the sum of the anticlockwise moments about any point in that plane."

This principle is based on the idea of rotational equilibrium, where the total turning effect (moment) from one direction (clockwise) is balanced by the total turning effect from the opposite direction (anticlockwise).

Mathematically:

$$\text{Total Anticlockwise Moment} = \text{Total Clockwise Moment}$$

This relationship ensures that the body remains in a state of equilibrium and does not rotate about the point in question.

This principle can be explained by considering two people on a seesaw.

The Principle of Moment in Daily Life

The moment of force is commonly used in various daily life activities. Some examples of its application include:

1. Applying a moment of force by hand to unscrew a stopper on a bottle.
2. Applying a moment of force using a spanner to unscrew a nut on a bolt.
3. Turning the steering wheel of a car, where a moment is applied to change the direction of the vehicle.

In these activities, the force applied is multiplied by the distance from the pivot point (the axis of rotation), making it easier to perform tasks like turning, unscrewing, or steering.