A moment of a force (also called a turning force or torque) is the ability of a force to rotate an body about a fixed point called the pivot or fulcrum.

The moment depends on two factors:

• The magnitude (size) of the force
• The perpendicular distance from the pivot to the line of action of the force

Formula

$M = F \times d$

Where:

• $M$ = moment of force (in Newton-meters, Nm)
• $F$ = force (in Newtons, N)
• $d$ = perpendicular distance from pivot to line of action (in meters, m)

Worked Example

A student weighs 400 N and sits 2 metres from the centre of a see-saw. What is the moment produced?

Solution: $M = F \times d = 400 \, \text{N} \times 2 \, \text{m} = 800 \, \text{Nm}$

This moment tends to rotate the see-saw clockwise (or anticlockwise depending on which side the student sits).

The Principle of Moments states:

If a body is in equilibrium under forces that lie in one plane, the sum of the clockwise moments equals the sum of the anticlockwise moments about any point in that plane.

Mathematically

$\text{Total clockwise moment} = \text{Total anticlockwise moment}$

Practical Application

Consider two children on a see-saw:

• Child A weighs 300 N and sits 2 m from the pivot
• Child B weighs 200 N and sits 3 m from the pivot

Moments:

• Child A: $300 \times 2 = 600 \, \text{Nm}$ (clockwise)
• Child B: $200 \times 3 = 600 \, \text{Nm}$ (anticlockwise)

Since both moments are equal, the see-saw balances. This is the principle of moments in action.

The centre of gravity (COG) of a body is the point at which the weight of the body appears to be concentrated. It is also the point where the resultant force of gravity acts on the body.

Key Points

1. For regularly-shaped objects with uniform density, the centre of gravity lies at the geometrical centre.
2. For irregular objects, the centre of gravity may lie outside the body (for example, in a hollow bowl).
3. An object will balance perfectly if supported at its centre of gravity.
4. The centre of gravity can be found experimentally by suspending an object from different points and marking where the lines of suspension meet.

Example in Daily Life

A Tanzania traditional mkono wa chai (tea tray) balances at its centre. If you place items unevenly on the tray, it will tip because the combined centre of gravity no longer lies above the point of support.

There are three main types of equilibrium:

1. Stable Equilibrium

A body is in stable equilibrium when, after being displaced slightly, it returns to its original position. This happens because the centre of gravity rises during displacement, creating a restoring force.

Example: A book resting on a flat table. If tilted slightly, it returns to its flat position.

2. Unstable Equilibrium

A body is in unstable equilibrium when, after a small displacement, it moves further away from its original position. The centre of gravity is lowered, causing the body to topple.

Example: A pencil balanced vertically on its tip. Any small disturbance causes it to fall.

3. Neutral Equilibrium

A body is in neutral equilibrium when a small displacement does not change the height of its centre of gravity. The body remains at rest in its new position.

Example: A round bottle (like a soda bottle) rolled on a flat surface. It comes to rest in any new position without tipping.

An object's stability depends on two main factors:

1. Lowering the Centre of Gravity: The lower the centre of gravity, the more stable the object. A low centre of gravity makes it harder for the object to tip over.

2. Widening the Base: A wider base provides greater stability because the line of action of weight stays within the base area for larger angles of tilt.

Real-life Examples

• Racing cars have low centres of gravity to prevent rolling over during sharp turns.
• Bunsen burners in the laboratory have wide bases to avoid tipping.
• Ships have deep keels (heavy weights at the bottom) to lower the centre of gravity and resist overturning in rough seas.
• Matatu (public transport) in Tanzania are more stable when luggage is stored low in the boot, not on the roof.

In Tanzania, the principle of moments is applied when using a spanner (rench) to unscrew a tight nut on a bicycle wheel or motorcycle. A longer spanner provides greater turning effect (moment) with the same force, making it easier to loosen stubborn nuts. Similarly, when loading a dala dala (minibus), luggage is placed low and near the wheels to keep the centre of gravity low and prevent the vehicle from overturning on bumpy Tanzanian roads.