**Equilibrium of forces**

**(A) Principle of Moments**

The principle of moments states that if a body is equilibrium then the sum of the clockwise turning moments acting upon it about any point equals the sum of the anticlockwise turning moments about the same point.

**Note:** some of moments = F_{2} x_{2 }– F_{1}x_{1 }= 0,

Or F_{1}x_{1} = F_{2}x_{2 }

**Moments of a force/torque**

The moment of a force about a point is defined as the product of the force and the perpendicular distance from the point to the line of action of the force. Moment = *Fxh* sin ~~O~~.

**Couples**

A couple is a system of two parallel and equal but opposite forces not acting along the same lines.

The turning moment of a couple is the product of one of the forces and the perpendicular distance between the lines of action of the two forces.example of couple can be seen in the action of a corkscrew, or turning a water tap on or off.

Picture of a water tap

Source: www.publicdomainvectors.org

Picture of a corkscrew

Source: www.common.wikimedia.org

**(B)conditions for equilibrium of rigid bodies under the action of parallel and non-parallel forces**

***For the action of parallel coplanar forces**

I.The algebraic sum of the forces acting on the body in any direction must be zero. In other words, the sum of upward forces must be equal to the sum of downward forces, and similarly for those forces along the other directions.

II.Moments: The algebraic sum of the moments of all the forces acting about any point must be zero; the sum of clockwise moments about any point must be equal to the sum of anticlockwise moments about the same points.(the principle is also known as the **principle of moments**).

***For the action of non-parallel forces coplanar forces**

I.The algebraic sum of the horizontal components equals zero. £_{x} = 0

The algebraic sum of the vertical components equals zero.£_{x} = 0

II.Moments: The algebraic sum of the moments of all the forces about any point in the plane must be zero. That is, the sum of the clockwise moments must be equal to the sum of anticlockwise moments about the same point.

**Notes:** equilibrium of a large body or long body tend to move the body in a straight line, but they can also have the effect of causing rotation. We have to consider moments as well.

**The triangle of forces**

When a body is in equilibrium under the action of three forces all acting in the same plane, the three forces can be represented in magnitude, direction and sense by the three sides of a triangle taken in order.

**Stability of a body: Types of equilibrium**

*Stable equilibrium*

A body is said to be in a position of stable equilibrium when, on receiving a slight displacement, it tends to its original position.eg. a rolling ball maintaining its original position.

Diagram of a stable equilibrium

Source: www.commons.wikimedia.org

*Unstable equilibrium*

A body is said to be in position of unstable equilibrium when, on receiving a slight displacement, it tends to move on, farther away from its original position.eg. a ball standing on a curve edge.

Diagram of unstable equilibrium

Source: www.commons.wikimedia.org.

**Effect of position of center of gravity on stability**

Diagram of the stability of a chair

Source: www.commons.wikimedia.com

A low armchair is more stable than a high chair or a tall stool. A chair which is normally quite stable can be put into an unstable position by tilting it back on its legs.

**Questions**

- Defined movement of a force ?

**Answer:** Moment of force about a point is defined as the product of the force and the perpendicular distance from the point to the line of action of the force.

- Defined the system couple?

**Answer:** A couple is a system of two parallel and equal but opposite forces not acting along the same lines.

- Explain the concept of stable equilibrium

**Answer:** A body is said to be in a position of stable equilibrium, when on receiving a slight displacement it tends to return to its original position.

- Mention the three(3) types of equilibrium end explain them

**Answer:**

Stable equilibrium: a body is said to be in a position of stable equilibrium when on receiving a slight displacement it tends to return to its original position.

Unstable equilibrium: a body is said to be in position of unstable equilibrium when on receiving a slight displacement it tends to move on, farther away from its original position.

Neutral equilibrium: a body is in equilibrium when on receiving a slight displacement it tends to come to rest in its new position.

- Name two examples of couples in concept of equilibrium

**Answer:** I. A water tap II. A corkscrew

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