 # Interesting facts about special theory of relativity and coordinate transformation

Introduction

1. In today’s article, we are going to study about ‘ Interesting facts about special theory of relativity and coordinate transformation ‘ How beneficial it is and what are the postulates of special theory of relativity. We will also read about some more topics like basic information about relativity, types of relativity, special theory of relativity , frame of reference, inertial frame of reference, non-inertial frame of reference, transformation equation for having translation etc in Detail.  So, take your notebooks in you hand and get ready to study physics in an easy and sorted way

# Relativity

The Theory which deals with the relativity of objects is known as theory of relativity. It is divided into two parts.

1. Special theory of relativity (1905)
2. General theory of relativity (1915)

Both theory are proposed by Einstein.

1. # Special theory of relativity

In this theory Newton’s first and second law both are valid. Here the motion remains constant or uniform. It is simpler.

## Postulates of STR or principle of special theory of relativity

1. Laws of physics are same in all frame inertial frame of reference. This is also called principle of relativity.
2. In free space velocity of light remains constant. That means it is universal constant For all frame of reference. And its value is 3×10^8 m/s. It doesn’t depend on the position of observer.

### Frame of reference (FOR)

A co-ordinate system from which we can describe the position or motion of a particle is called frame of reference.

There are two types of frame of reference

1. Inertial
2. Non- inertial

### Inertial

In which first and second laws are valid and remains in uniform motion. If external force is zero then velocity remains constant I=0, ma=0, a=0 and v→constant

### Non inertial

In which Newton’s first and second laws are not valid. Motion will be rotated and accelerated even in the absence of force.

Example- Earth (inertial frame of reference)

a= ω^2R

a= (2π/24×60×60)^2 ×6.4× 10^6

And a= 3.4× 10^-2 m/sec^2

#### Co-ordinate transformation

1) Transformation equation for frame of reference having translation- Here s is stationary frame of reference. And S’ is moving frame of reference. From vector addition we have,

ro + r’ = r

Then r’ = r – ro   …(1)

Differentiating this equation with respect to time t’

dr’/dt = dr/dt – dro/ dt

v’ = v- 0 (∴ ro= constant)

v’ = v                 …(2)

v= velocity of object with respect to s frame of reference.

v’ = velocity of particle with respect to s’ frame of reference.

Again differentiating the equation (2) with respect to t, we get

dv’/dt = dv/dt

Then, a’ = a

That means acceleration remains constant.

#### 2) transformation equation in frame of reference having uniform relative motion of translation-

At time t=0 After time t= 0 or at time t. Let us suppose that s’ frame is moving with constant velocity with respect to s frame. Thus at time t, we have

ro= vt    …(3)

(Distance travelled in time t by moving frame of reference)

From diagram we have,

ro + r’ = r

vt + r’ = r

And hence, r’ = r- vt   …(4)

Now differentiating equation (4) with respect to time t,

dr’/ dt = dr/dt + v

v’ = v- V              …(5)

v’ is velocity of particle with respect to s’ frame of reference.

And V is velocity of particle with respect to s frame of reference

v is velocity of s’ frame.

Again differentiating with respect to time,

dv’/dt = dv/dt – 0

Where v is constant

I.e. a’ = a

But acceleration remains constant.

##### Conclusion

So our article is finished and after completely reading this article, one can easily tell what is special theory of relativity. And we have also discussed some more topics like postulates of STR, types of frame of reference, co-ordinate transformation etc.

‌So one can say that they got a detailed information about special theory of relativity, and basic information about other topics.

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