## 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 × perpendicular distance from pivot.

## The law of moments

The law of moments 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).

Examples

- 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? - 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,

Clockwise moments = 10 × 30 = 300 N cm, 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.

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

Solution

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

Anticlockwise moments = (20 × 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. We use the law of moments in the operation of levers.

Example

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

Solution

Taking moments about O. Then, clockwise moments = effort × 200 cm. Anticlockwise moments = 200 × 30 cm.

Effort = (200 × 30)/ 200 = 30 N.