**1.0**

**Forces in equilibrium**

**1.1**

**Moment of a force**

**Turning effect of force**

**Turning force –**is the force that causes an object to rotate or turn about a fixed point.

**Moment –**is the turning effect of force

**Note:**T he hinges of the door represent a turning point called the

**pivot**or

**fulcrum.**

**Moment of a force about a point**–is the product of the force and the perpendicular distance of its line of action from the point.

Hence,

The SI-unit of moment of force is Newton metre (Nm)

**Principle of moments**

State the principle of moment

**Principle of moment state that**” for a system in equilibrium, the total clockwise moment must be equal to the total anticlockwise moment.

Mathematically,

Also can be written as

**1.2**

**Centre of gravity**

**Centre of gravity of a body**

**Centre of gravity of a regular object**

**The centre of gravity (c.g) of an extended body**–is the point where the force of gravity can be considered to act

**1.3**

**Types of equilibrium**

**Equilibrium**

**Equilibrium**is the state of balance of a body.

Examples of objects which are in a state of balance

1. A book lying on a desk

2. A passenger walking at the back of a train (coach) while the train is moving

3. An acrobat balancing on a tightrope

**Conditions for equilibrium**

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**Equilibrium conditions can be in relation to:** i. Rotational

ii. Static

iii. Dynamic or translation

**Static equilibrium**–is a condition of balance of a body when it is stationary (not moving at all)

**Dynamic equilibrium**–is a condition of balance of a body when it is moving

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**The conditions for equilibrium depend on three characteristics of forces** i. Magnitude

ii. Direction of forces

iii. Point of application

**The conditions for a body to be in equilibrium**

1. The sum of the forces in one direction must be equal the sum of the forces in the opposite direction

2. Anticlockwise moments = clockwise moments.

**Types of equilibrium are:**

**1.**

**Stable equilibrium**–is the steady state of balance of a body

**Conditions for a body to be stable**

i. The area of the base must be large

ii. The centre of gravity has to be low

**2.**

**Unstable equilibrium**–is the unsteady state of balance of a body

**3.**

**Neutral equilibrium**–is a state of balance in which a body remains in its position until displaced.

**Applications of equilibrium**

i. In stable cars and trucks have cambered wheels (wide wheelbases) and low centres of gravity

ii. The chases and engines are placed low in vehicles so as to increase the stability of the vehicles

iii. The luggage in the buses is at bottom so as lowers the centre of gravity to make more buses stable.

iv. Stable equilibrium helps in tall structures such as building and pylons

v. In unstable equilibrium helps in the act of walking.

vi. Neutral equilibrium helps in playing billiards (pool table)

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