## Turning Effects

- The turning effect of a body is called the moment of that force.- The turning effect produced depends on both the size of the force and the distance from the pivot.

- The moment of a force about a point is the product of the force applied and the perpendicular distance from the pivot (or turning point) to the line of action of the force.

Hence,

**Moments of a force = Force x perpendicular distance from pivot**.

### The Law of Moments

- It states that

*when a body is in balance or in equilibrium, the sum of the clockwise moments equals the sum of anti-clockwise moments.*- The SI units of the moments of a force is

**Newton metre (Nm).**

**Example 1**

1. A uniform rod of negligible mass balances when a weight of 3 N is at A, weight of 3 N is at B and a weight of W is at C. What is the value of weight W?

*Solution*

Taking moments about the fulcrum, O then

Anti-clockwise moments = (3 x 1) + (3 x 3)

= 3 + 9 = 12 Nm

Anti-clockwise moments = clockwise moments

3 W = 12 Nm

W = 4 N

**Example 2**

2. The following bar is of negligible weight. Determine the value of ‘x’ if the bar is balanced.

*Solution*

The distance from the turning point to the line of action can be determined as;

Anticlockwise moments = 10 × ‘x’ = 10 x. N cm.

Using the principle of moments

Anti-clockwise moments = clockwise moments

10 x = 300, hence x = 30 cm.

**Example 3**

3. Study the diagram below and determine the value of X and hence the length of the bar.

*Solution*

Clockwise moments = 15x N + 5(X x 20) N

Anticlockwise moments = (20 x 10) + (60 × 10) N cm = 800 N cm.

Anti-clockwise moments = clockwise moments

800 N cm = 15X + 5X + 100

800 n cm = 20X + 100

20X = 700

X = 35 cm.

Therefore, the length of the bar = 40 + 20 + 35 + 20 = 115 cm.

## The Lever

-A lever is any device which can turn about a pivot or fulcrum.-The applied force is called the effort and is used to overcome the resisting force called the load.

**Example 4**

Consider the following diagram. (The bar is of negligible mass). Determine the effort applied.

*Solution*

Taking moments about O. Then, clockwise moments = effort x 200 cm.

Anticlockwise moments = 200 x 30 cm.

Effort = (200 x 30)/ 200 = 30 N.