Moments

Definition

The moment of a force is the measure of the turning effect of a force about a point or axis.

It is calculated as:

Moment = Force × Perpendicular distance from the pivot

$$M = F \times d$$

Where:

M

• = moment

F

• = applied force

d

• = perpendicular distance from the pivot or axis of rotation

The SI unit of moment is newton metre (N m).

A moment is said to be:

Clockwise

• if it tends to rotate an object in the clockwise direction

Anticlockwise

• if it tends to rotate an object in the opposite direction

Main Content

1. Turning Effect of Force

• A force does not always cause motion in a straight line; it can also cause rotation. This rotational effect is called the turning effect of force or moment.
• The size of the turning effect depends on both the magnitude of the force and how far the force acts from the pivot. For example, pushing a door near the handle creates a larger moment than pushing near the hinges because the distance from the pivot is greater.

The turning effect is easy to observe in daily life:

• A wrench loosening a bolt
• A bicycle pedal turning the chain
• A child sitting farther from the center of a seesaw making it easier to tilt

The greater the perpendicular distance from the pivot, the greater the turning effect for the same force. This is why tools like crowbars and spanners are designed with long handles.

2. Principle of Moments

• The principle of moments states that when a body is in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
• This principle is essential for analyzing balance in objects such as balanced beams, weighing scales, and bridges.

Mathematically, for equilibrium:

$$\text{Sum of clockwise moments} = \text{Sum of anticlockwise moments}$$

This can also be written as:

$$\sum M_{\text{clockwise}} = \sum M_{\text{anticlockwise}}$$

If the clockwise and anticlockwise moments are not equal, the body will rotate. This principle is used in designing stable structures and solving balance problems.

Example:

• If a 10 N force acts 2 m from a pivot clockwise, the moment is 20 N m.
• To balance it, an anticlockwise moment of 20 N m is needed, such as a 5 N force acting 4 m from the pivot.

3. Equilibrium and Balance

• A body is in rotational equilibrium when the net moment acting on it is zero. This means there is no tendency to rotate clockwise or anticlockwise.
• Equilibrium is important in ensuring that structures remain stable and objects do not topple unexpectedly.

There are two main ideas related to balance:

Translational equilibrium

• : the net force is zero, so the object does not move linearly

Rotational equilibrium

• : the net moment is zero, so the object does not rotate

For complete equilibrium, both conditions must be satisfied.

Example of equilibrium: A seesaw is balanced when the product of force and distance on one side equals the product on the other side.

A simple balance arrangement:

      10 N                 5 N
       ↓                    ↓
--------|--------------------|--------
       2 m                  4 m
            Pivot

Here, both sides produce equal moments:

• Left side: 10 × 2 = 20 N m
• Right side: 5 × 4 = 20 N m

So the seesaw remains balanced.

Working / Process

1. Identify the pivot or axis of rotation

• First, determine the point about which the body may rotate. This may be a hinge, axle, support point, or center of turning.

2. Measure the perpendicular distance

• Find the shortest distance from the pivot to the line of action of the force. Only the perpendicular distance matters, not the slant distance.

3. Apply the moment formula and compare directions

• Calculate the moment using $M = F \times d$, then decide whether it is clockwise or anticlockwise. If multiple forces act, add clockwise moments and anticlockwise moments separately to check for balance.

Advantages / Applications

• Moments help explain and design tools and machines that multiply force, such as levers, pliers, wheelbarrows, and crowbars.
• They are essential in engineering and construction for analyzing beams, bridges, cranes, and structural stability.
• Moments are used in everyday balance situations, such as opening doors, using a seesaw, tightening bolts with a wrench, and balancing loads.

Summary

• A moment is the turning effect of a force about a pivot.
• It depends on force and perpendicular distance.
• Balanced objects have equal clockwise and anticlockwise moments.
• Important terms to remember: force, pivot, perpendicular distance, clockwise moment, anticlockwise moment, equilibrium.