**FORCES IN EQUILIBRIUM**

#### Moment of a Force

#### The Effects of Turning Forces

in motion or making it move if it was at rest.

If a body under the action of a net external force is allowed to rotate about a pivot, the body will tend to turn in the direction of the applied force.

**Examples of turning effect of force:**

A person pushing a swing will make the swing rotate about its pivot.

A worker applies force to a spanner to rotate a nut.

A person removes a bottle’s cork by pushing down the bottle opener’s lever.

Force is applied to a door knob and the door swings open about its hinge.

A driver can turn a steering wheel by applying force on its rim.

**The Moment of Force**

Moment of force** **about a point is the turning effect of the force about that point. It is obtained as the product of applied force and the perpendicular distance from the point of

**the application of the force.**

**Therefore, moment of a force depends on two factors namely;**

- The applied force.
- The perpendicular distance from the point of action of the force to the turning point(fulcrum).

The change of state of a body can appear in several forms and the most common form is the turning effect which is referred to as moment of a force.

The unit for the moment of a force is Newton-meter (Nm).

**The turning effect can bring about two kinds of moments;**

Clockwise moment -caused by the forces which tend to turn the body in a clockwise direction.

Anticlockwise moment -caused by the forces which tend to turn the body in an anticlockwise direction.

**Consider the diagram below,**

The above uniform rod AB is balanced about the turning point (fulcrum) f. The weight W_{1} acting at point A tends to turn the rod in anticlockwise direction. The weight W_{2} acting at point B and the weight of the rigid body W_{0} tends to move the rod in clockwise direction. Hence, we have two anticlockwise moments due to weight W_{2} and weight of the rod W_{0}.

**The Principle of Moments**

The Principle of moments states that:

*” If a body is in equilibrium under action of forces which lie on one plane, then, the sum of the clockwise moments is equal to the sum of the anticlockwise moments about any point in that plane.”*

**The equilibrium of state of a body is brought about by two conditions;**

- The sum of anticlockwise moments is equal to sum of clockwise moments about the turning point.
- The sum of upward forces is equal to sum of downward forces acting on a body.

If the data for the weight (force) *W*, and distance *d* of the weight from the fulcrum can be obtained then the moment created about the fulcrum is obtained by multiplying the weight with the respective distance i.e *Wd*. According to the principle of moments, at equilibrium the sum of clockwise moments (*Wd*) and that of anticlockwise moments (*Wd*) must be equal. to make it simple the below table can be used to record and compare the moments;

W_{1}(g) |
W_{2}(g) |
d_{1}(cm) |
d_{2}(cm) |
W_{1}d_{1}(gcm) |
W_{2}d_{2}(gcm) |

Materials and apparatus:Meter rule, several different weights, inelastic cotton thread, knife edge and a marker pen.

**Procedures**

Balance the meter rule horizontally on a knife edge.

Mark a balance point as C. Use the marker pen to do that.

Suspend a meter rule from a fixed axis through C. Suspend unequal weights W₁ and W₂ from the meter rule by using thin cotton threads.

Adjust the distance d₁ and d₂ of the weights W₁ and W₂ from C until the meter rule balance.

Repeat the experiment five times using different values of W₁ and W₂.Record the results on the table as shown below.

W₁(g) | W₂(g) | d₁(cm) | d₂(cm) | W₁ d₁ (gcm) | W₂ d₂ (gcm) |

Observation:In each case it will be found that W₁ d₁ is equal to W₂ d₂.

The Principle of Moment in Daily Life

**Moment of a force is used in the following:**

Is applied by a hand to unscrew a stopper on the bottle.

Is applied by a spanner to unscrew a nut on a bottle.

Turning a steering wheel of a car.

**Centre of Gravity**

**Center of gravity** of a body is the point at which the weight of a body appears to be concentrated. OR center of gravity of a body is the point of application of the resultant force due to the earth attraction on the body.The center of gravity of a regular body is found to be at its geometrical center.

**Example 1**

- Centre of gravity of a uniform meter rule is at the 50cm mark.
- Centre of gravity of a circular object is at its center.

The center of gravity of irregular bodies can be found experimentally.

**Types of Equilibrium**

The Condition for Equilibrium

Equilibrium is simply the state of balance of a body. A body is said to be balanced if its center of gravity is directly above the point of support.

The body is more stable when its center of gravity is closer to its base and if it has a wide base.

The body can be in motion while in equilibrium state. Equilibrium of this type is known as dynamic equilibrium.

A body in state of rest while in equilibrium is under static equilibrium while the one which is rotating but still in equilibrium is said to be under rotational equilibrium.

Stable, Unstable and Neutral Equilibrium

**There are three types of equilibrium, namely:**

- Stable equilibrium
- Unstable equilibrium
- Neutral equilibrium

**Stable equilibrium:**A body is said to be in stable equilibrium if is given with small displacement the center of gravity will be raised and the body returns to its original position after displacement.

**Unstable equilibrium:**A body is said to be in unstable equilibrium if when given a small displacement the center of gravity will be lowered and the body doesn’t returns to its original position after displacement.

**Neutral equilibrium:**A body is said to be in neutral equilibrium when a small displacement doesn’t alter the position of the center of gravity; the body is at rest in whichever position it is placed, eg, rolling a sphere or a barrel.

Conditions of Stable, Unstable and Neutral Equilibrium in Daily Life

**Application of turning effect in daily life**

Is applied by a hand to unscrew a stopper on the bottle.

Is applied by a spanner to unscrew a nut on a bottle.

Turning a steering wheel of a car.

**Exercise 1**

.The moment of a force about a point is 1120 Nm.If the magnitude of the force is 5600N,find the perpendicular distance between the point and the line of action of the force