(d) Turning effect of forces

Learning Objectives

• define and apply the moment of a force and give everyday examples

• recall and apply the relationship moment of a force  = force x perpendicular distance from the pivot to new situations or to solve related problems

• show an understanding that a couple is a pair of forces which tends to produce rotation only.

• show an understanding that, when there is no resultant force and no resultant torque, a system is in equilibrium.

• state the principle of moments for a body in equilibrium

• apply the principle of moments to new situations or to solve related problems.

• show understanding that the weight of a body may be taken as acting at a single point known as its centre of gravity

• describe qualitatively the effect of the position of the centre of gravity on the stability of objects

In Sec 3, you learned how forces affect motion. In this topic on Moment of a force , you will learn how force can cause turning to take place about a point.

Moments

• The moment of a force is the turning effect of the force about a fixed point known as the fulcrum or pivot.

• Everyday examples of turning effect of a force

• The moment of a force about a pivot is the product of the force, and the perpendicular distance, d, from the line of action of the force to the pivot.

• Moment of a force about a pivot = F x d

• The SI unit for momnet is the newton metre (Nm)

• The moment of the force is proportional to :

• the magnitude of the force, and

• the perpendicular distance from the pivot to the line of action of the force

• A moment may be clockwise or anticlockwise depending on the direction of its turning effect.

• The principle of moments states that when a body is in equilibrium, the total clockwise moments about any point is equal to the total anticlockwise moments about the same point.

Examples

1. A uniform metre rule is pivoted at its centre. It is balanced by two weights, 40 N and 20 N. Find the distance of the 20 N weight from the pivot.

2. The figure shows a uniform plank of mass 5.0 kg and length 3.00 m resting horizontally on two trestles, P and Q, which are a distance of 2.50 m apart. When a student of mass 60.0 kg walks along the plank from one trestle to the other, the plank sags.

Calculate the downwards force exerted on each trestle when the student is a distance

of (a)0.50 m from trestle P and (b) 1.25 m from trestle P.

• If a body is in equilibrium, it does not move.

For a body to be in equilibrium,

* the sum of the forces acting in one direction must equal the sum of forces acting in the opposite direction.

* it must obeys the principle of moments.

Centre of mass and centre of gravity

• The centre of mass of a body is the point at which the whole mass of the body seems to concentrate.

• The centre of gravity of a body is the point at which the whole weight of the body seems to act.

• For a regular body, the centre of gravity lies in its centre.

• The centre of gravity need not be in a solid part of a body.

• Centre of gravity of an irregular shaped lamina

• In a uniform gravitational field, the centre of mass of a body coincides with its centre of gravity.

Why doesn't the leaning tower of pisa topple over?

• The stability of a body is its ability to return to its original position when the body is displaced slightly and then released.

• If the body is displaced such that its centre of gravity falls within its base area and is then released, the body will return to its original position. The body is said to be stable.

• If the body is displaced such that its centre of gravity falls outside its base area and is then released, the body will topple. The body is said to be unstable.

The stability of a body is increased by :

• A stable body might have a low centre of gravity and a broad base.

There are three types of equilibrium.

• In stable equilibrium, a body returns to the original position when it is displaced slightly and then released.

• In stable equilibrium, any displacement raise the centre of gravity of the body.

• In unstable equilibrium, a body topples when it is displaced slightly and then released.

• In unstable equilibrium, any displacement lowers the centre of gravity of the body. 

• In neutral equilibrium, a body that is displaced slightly stops at a new position with its centre of gravity neither raised nor lowered.

• Any displacement neither raises nor lowers the centre of gravity of a body in neutral equilibrium.