# Introduction

In this particular article Physical laws and frame of reference we will study about the frame of reference ,its theory along with its derivations.The branch of physics which describes the behaviour of physical bodies, when subjected to force or displacements, and the Subsequent effect of bodies on their environment is called **mechanics.** Mechanics can be divided into two parts-

- Statics – In which we studies about force acting on particles when they are in rest position under equilibrium condition.
- Dynamics- In which we study particles when they are in motion.

## Relativity

The theory which deals with the relativity of objects is known as theory of relativity.and it can be divided into two parts

- Special theory of relativity (1905)
- General theory of relativity (1915)

Both theories are proposed by Einstein.

### Simple theory of relativity

In this theory Newton’s first and second laws are Valid. In this theory motion of particle remains constant or uniform . So It is simpler.

#### Postulates or principle’s of simple theory of relativity (STR)

- Laws of physics are same in all inertial frame of reference. This is also called principle of relativity.
- In free space velocity of light remains constant, that means it is universal constant for all frame of reference and its value is 3 ×10⁸ m/s. It doesn’t depend on the position of observer.

##### Physical laws and frame of reference (F.O.R)

A coordinate 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 frame of reference :-

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

F = m(d²r/dt²) =0

m(d²r/dt²) =0

(d²r/dt²) =0

Hence above equation ,in form of components can be written as

(d²x/dt²) =0

(d²y/dt²) =0

(d²r/dt²) =0

So, Now integrate above equation with respect to time t,

dx/dt= Vx=constant

And dy/dt=Vy=constant

Also, dz/dt= Vz= constant

Hence, from above equation we can say that in absence of external applied force , velocity of particle remains constant.

2) Non-inertial frame of reference :- In which Newton’s first and second laws are not valid . As a result Motion will be rotated and accelerated even in the absence of external applied force. All accelerated and rotating frame of reference are Non-inertial frame of reference . For example- earth rotates on its own axis and all frame of reference present on earth is Non-inertial frame of reference. But value of acceleration due to rational motion of earth is very low . hence due This reason frame of reference present on earth is taken as Inertial frame of reference.

a=ω²R

a =(2π/24×60×60)×6.4×10⁶

a= 3.4×10⁻² m/s

###### Particle or event in Cartesian co-ordinate frame of reference

The position of particle in a system can be described by a Cartesian coordinate system. Let O is reference point .let at any time t₁, particle is at point P. And its coordinate is (x₁,y₁,z₁). If the position vector ofopoint P is r₁ then,

r₁ = x₁iˆ+ y₁jˆ+ z₁kˆ (1)

Let at time t₂ particle reaches at point Q fromopoint P. And coordinates at point Q is (x₂,y₂,z₂) and if position vector is r₂ then,

r₂=x₂iˆ+ y₂jˆ+ zk₂ˆ

Then difference in time (t₂-t₁) = ∆t

And now , in triangle OPQ

OQ = OP + PQ

Or, PQ = OQ -OP

PQ = r₂-r₁ = ∆r (3)

The total displacement of the particle is ∆r and ∆t is the time it takes to travel this distance. Hence the ratio of this displacement and time is called velocity and it is denoted by ‘v’.

Then the average velocity is given by v= r₂-r₁/t₂-t₁ =∆r/∆t (4)

If ∆t →0 then the rate of change of displacement is called instantaneous velocity or velocity.

v = Lim ∆t→0 (∆r /∆t) = dr/dt = (dx/dt)iˆ+ (dy/dt)jˆ+ (dz/ dt)kˆ (5)

If velocity changes with time or at t₁ time velocity is v₁ and for t₂ time velocity is v₂ then as a result, The above equation becomes

Average acceleration of the particle a= v₂-v₁/t₂-t₁ = ∆v/∆t (6)

Again if ∆t→0, then the rate of change of velocity is called instantaneous acceleration.

###### Conclusion

In this article Physical laws and frame of reference, we have studied basics of mechanics, special theory of relativity and its postulates, frame of reference, Inertial frame of reference and frame of Non-inertial reference etc in most simplest manner.