Basic Concept of Vector and Scalars Quantities

Basic Concept of Vector:

1. Introduction

In engineering, frequent use is made of physical quantities, such as force, speed, and time. For example, we talk of the speed of a car, and the force in a compressed spring.

 It is useful to separate physical quantities into two types: the first are called scalars; the second are known as vectors. A scalar is a quantity that can be fully described by a single number known as the magnitude.An example of a scalar quantity is the mass of an object, so we might state that ‘the mass of the stone is 3 kg’. It is important to give the units in which the quantity is measured. Obvious examples of scalars are temperature and length, but there are many other engineering applications in which scalars play an important role. For example, speed, work, voltage and energy are all scalars. On the other hand, vectors are quantities which require the specification of a direction, in addition to a magnitude, before they are completely described. An example of a vector quantity is the force applied to an object to make it move. When the object  is moved by applying a force to it we can achieve different effects by applying the force in different directions.

 A force is a vector quantity. Applying the force in a different direction will achieve a different effect.

In order to specify the force completely we must state not only its magnitude (its ‘strength’) but also the direction in which the force acts. For example we might state that ‘a force of 5 newtons is applied vertically from above’. Clearly this force would have a different effect from one applied horizontally. The direction in which the force acts is crucial. There are many engineering applications where vectors are important.

Force, acceleration, velocity, and electric or magnetic fields are all described by vectors. Furthermore, when computer software is written to control the position of a robot, the position is described by vectors. Sometimes confusion can arise because words used in general conversation have specific technical meanings when used in engineering calculations. An example is the use of the words ‘speed’ and ‘velocity’. In everyday conversation these words have the same meaning and are used interchangeably. However in more precise language they are not the same. Speed is a scalar quantity described by giving a single number in appropriate units;

For example ‘the speed of the car is 40 kilometres per hour’. On the other hand velocity is a vector quantity and must be specified by giving a direction as well. For example ‘the velocity of the aircraft is 20 metres per second due north’. In engineering calculations, the words speed and velocity should certainly not be used interchangeably. Similar problems arise from use of the words ‘mass’ and ‘weight’. Mass is a scalar which describes the amount of substance in an object. The unit of mass is the kilogramme. Weight is a vector, the direction of which, is vertically downwards. Weight arises from the action of gravity. The unit of weight is the newton. 

quantities which can also cause confusion. Whereas distance is a scalar, displacement is ‘directed distance’, that is, distance together with a specified direction.
 So, if an object is moved from point A to point B, we can state that the distance moved is 10 metres, but the displacement is 10 metres in the direction from A to B.
AB
10m

You will meet many other quantities in the course of your studies and it will be helpful to know which are vectors and which are scalars.


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You will meet many other quantities in the course of your studies and it will be helpful to know which are vectors and which are scalars.
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