Mathematical Physics

 Lesson No 02. Mathematical Physics

🕮 Introduction

In previous lessons, we have studied various physical quantities which can be measured. But all these quantities cannot be fully described by measurements and units only. There is a need to do perform a mathematical operation to obtain the desired results.This physical quantity is described fully using magnitude, direction, or both. In order to describe Physical Quantity, it has been categorized into two types:

a) Scalar Quantity

b) Vector Quantity

    🕮 Scalar Quantity

Scalar Quantity: Any physical quantity that depends only on the magnitude and not on direction is called Scalar Quantity. Eg: Mass, Work, etc

Let us consider an example, A person carrying 5kg sugar wants to go to a particular distance B. He can reach that point by going in any didirectionrecon. After reaching point B the mass 5 kg remains unchanged, thus it does not depend on direction, hence mass is a scalar quantity.

Scalar quantity can be added, subtracted, multiplied, divided by simple mathematical operations we use in our day to day-to day-to-day-day day life.

🕮 Vector Quantity

Vector quantity: Any physical quantity that depends on the magnitude, as well as direction, is called as Vector Quantity. Eg: Force, Torque, Velocity, etc

Let us consider an example, for opening a particular door, a minimum 5N force is required and it should be pulled but if a person is applying 5N force and he is pushing it instead of pulling, then the door will not be opened. On the other hand, if a person is pulling it but applying force less than 5N , again door will not be opened. So we can conclude that if we do not take magnitude as well as direction into consideration, we do not obtain the output, thus force depends on the magnitude as well as direction, hence Force is a vector quantity.

🕮 Representation of a Vector

A vector quantity is represented by a directed line segment or we can say ‘arrow’.Let a person moves from point A to B, then it can be represented as,

                               AB

where A is the starting point of the person called as the tail of the vector and B is the endpoint called as head of the vector. It can be written as

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_{│<<<Types of vector│}                

_{Related topics: Mathematical physics      Types of the vector    Vector operation}   

 _{Triangle laws of vector addition       Parallelogram laws of vector addition} 

  _{Resolution of  a vector         Scalar multiplication   Vector multiplication}

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