Sunday, October 17, 2021

What Is An Inertial Frame Of Reference In Physics

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Distant Stars As Inertial Frames:

Relative Motion and Inertial Reference Frames

We consider the very distant stars as inertial frames. You will ask how can they be; as they must also move around some galaxy or something. But their velocity from this far off distance on our planet appears to be really negligible. So, any rigid body that is far off from our planet in deep interstellar space can be taken as an inertial frame of reference.

Inertial Frames In Newtonian Spacetime

By the early years of the 20th century, the notion ofinertial system seems to have been widely accepted as the basis forNewtonian mechanics, even if the specific works of Lange and Thomsonwere little noticed. In writing On the electrodynamics ofmoving bodies in 1905, Einstein took it to be obvious to hisreaders that classical mechanics does not require a single privilegedframe of reference, but an equivalence-class of frames, all in uniformmotion relative to each other, and in any of which theequations of mechanics hold good. Two inertial frames withcoordinates \\) and \\) are related bythe Galilean transformations,

. These transformations clearly preserve the invariantquantities of Newtonian mechanics, i.e. acceleration, force, and mass. As far as Newtonianmechanics was concerned, then, the problem of absolute motion wascompletely solved; all that remained was to express the equivalence ofinertial frames in a simpler geometrical structure.

The lack of a privileged spatial frame, combined with the obviousexistence of privileged states of motionpaths defined asrectilinear in space and uniform with respect to timesuggeststhat the geometrical situation ought to be regarded from afour-dimensional spatio-temporal point of view.;Thestructure defined by the class of inertial frames can be captured inthe statement that space-time is a four-dimensional affinespace, whose straight lines are the trajectories ofparticles in uniform rectilinear motion. See Figure 4.

Figure 6

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  • A frame of reference that moves with constant velocity with respect to an inertial frame is also an inertial frame.For example: Newton’s laws work in the physics lab, which is fixed to the Earth. Therefore they also work in a train moving with constant velocity with respect to the Earth.
  • If the laws of mechanics work in one frame of reference, then they also work in a frame of reference that moves with constant velocity with respect to the first frame. If you can juggle on the platform, you can juggle in the train, or even in a plane, even if a bystander sees you and the balls whizzing by at high speed.

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What Is An Inertial Frame Of Reference

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what is an inertial frame of reference ?Simple ?

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it’s the immediate space-time co-oridinate in which the observer is not in motion.

with constant velocity along a straight line and without rotation.

meopemuk:rotation respect to what ?

The reference frame should not spin around its own axis

distant stars should not be seen in a circular motion

Actually,…… it is such a fundamental notion in physics, than it cannot be reduced to anything simpler. However, I don’t think there is any controversy. We will all agree whether the frame is inertial or not when we see it.

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definesas seen from an inertial observer

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To me, in the classical physics context, fictitious forces are “forces” that have no agent.

That’s the centripetal force that causes the object to accelerate continuously towards the center of its circular path, in an inertial reference frame. It’s very real.I’m talking about the centrifugal force that apparently pulls the object outwards, in a rotating reference frame. The rope can’t pull or push outwards on the object.

Frame Of Reference Examples

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Below are some examples of frame of reference, from which youll clearly understand the exact meaning of a frame of reference.

  • While riding a skateboard,a skateboard is the frame of reference
  • While driving a car, a car is the frame of reference
  • While sitting inside a moving train, a train is the frame of reference
  • While flying in an aeroplane, an aeroplane is the frame of reference

All these are examples of frame of reference.

Lets understand the above examples in detail, so youll get an exact idea.

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The Lingering Problem Of Absolute Space

Newton understood the Galilean principle of relativity with a degreeof depth and clarity that eluded most of his relativistcontemporaries and critics. It may seem bizarre, therefore, that thenotion of inertial frame did not emerge until more than a century anda half after his death. He had identified a distinguished class ofdynamically equivalent relative spaces, in any of whichtrue forces and masses, accelerations and rotations, would have thesame objectively measured values. Yet these spaces, though dynamicallyequivalent and empirically indistinguishable, were yet not equivalentin principle. Evidently, Newton conceived them as moving with variousvelocities in absolute space, though those velocities could not beknown. Why should not he, or someone, have recognized the equivalenceof these spaces, and the dispensability of a distinguished restingspaceabsolute spaceimmediately?

Meaning Of Inertial Frame Of Reference

Imagine, you are standing on a road, waiting for a car.

Suppose that you notice a car running on a road.

While standing on a road, why do you notice that car going forward?

Its because of your frame of reference.

Similarly,;

Imagine, you are standing on a terrace, looking at the sky.

Suppose that you notice an aeroplane flying in the sky.

While standing on a terrace, why do you notice that aeroplane moving forward?

Its because of your frame of reference.

In a similar way,

Suppose that you are sitting inside a truck which is moving with constant velocity.

While sitting inside a truck, why do you notice other vehicles moving on a road?

Again,;

In above cases,;

Because youre in an inertial frame of reference, youll notice a car, aeroplane and other vehicles moving.

The question is,

What is an inertial frame of reference?

Here,

Ill explain to you the exact meaning of an inertial frame of reference.

Lets quickly start off with the definition of inertial frame of reference.

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What Do You Mean By Inertial And Non Frame Of Reference

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Inertial Frame Of Reference

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In classical physics and special relativity, an inertial frame of reference is a frame of reference that is not undergoing acceleration. In an inertial frame of reference, a physical object with zero net force acting on it moves with a constant velocity or, equivalently, it is a frame of reference in which Newton’s first law of motion holds. An inertial frame of reference can be defined in analytical terms as a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. Conceptually, the physics of a system in an inertial frame have no causes external to the system. An inertial frame of reference may also be called an inertial reference frame, inertial frame, Galilean reference frame, or inertial space.

All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration. Measurements in one inertial frame can be converted to measurements in another by a simple transformation . In general relativity, in any region small enough for the curvature of spacetime and tidal forces to be negligible, one can find a set of inertial frames that approximately describe that region.

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Galilean Relativity In Newtonian Physics

Oddly enough, no one in the 17th century, or even beforethe late 19th century, expressed this equivalence ofreference-frames any more clearly than Newton himself. However, thecredit for articulating this equivalence precisely for the first time,belongs to Christiaan Huygens, who introduced it as one of theHypotheses of his first work on the rules of impact .Hypothesis I was the first clear statement of theprinciple of inertia: Any body, once in motion, if nothingopposes it, continues to move always with the same velocity and alongthe same straight line . The firstprecise statement of the relativity principle followed as HypothesisIII:

The motion of bodies, and their speeds equal or unequal, are to beunderstood respectively, in relation to other bodies which areconsidered as at rest, even though perhaps both the former and thelatter are subject to another motion that is common to them. Inconsequence, when two bodies collide with one another, even if bothtogether undergo another equable motion, they will move each other nodifferently, with respect to a body that is carried by the same commonmotion, than if this extraneous motion were absent from all of them..

Newtons first statement of the same principle appears in one ofthe series of papers that culminated in the Principia,De motu sphæricorum corporum in fluidis .Like Huygens, Newton presents the relativity principle as afundamental principle, Law 3:

What Is Inertial & Non Inertial Frame Of Reference

Frame of Reference :

A frame of reference is a set of coordinates with respect to which the motion of a body is analysed. Different types of coordinates may be used Rectangular Cartesian coordinates or Polar coordinates.

A frame of reference may be inertial or non-inertial and this has to be borne in mind when Newtons 2nd law of motion is applied to a body.

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A Bus Moving With Constant Velocity

Imagine, you are sitting inside a bus.

Suppose that a bus is moving with constant velocity on a road.

Now, let me ask you one question.

While sitting inside a bus, can you guess your frame of reference?

The answer is simple.

You are in an inertial frame of reference.

As you know, a bus moving with constant velocity doesnt mean that it is accelerated.

In short,

A frame of reference which is at rest or moving with constant velocity is known as inertial frame of reference

Thats how you can remember the definition of inertial frame of reference.

Is Earth An Inertial Or Non

Frame Of Reference Science Definition

From the definition of inertial frame of reference, it is clear that

When an objects frame of reference is not accelerated, an object is said to be in an inertial frame of reference.

Now,;

If we consider the object as earth, then what do you think about the frame of reference of earth?

Is earth an inertial frame of reference?

You might be thinking that earth is an inertial frame of reference, right?

If you are thinking so, you are wrong !!

Okay, lets make it simple.

Imagine, you are in space and looking at the earth.

Now what do you think, is earth an inertial or non-inertial frame of reference?

The answer is simple.

While watching from space, the frame of reference of earth appears to be accelerated.

So, earth is anon inertial frame of reference.

In both cases, the earths frame of reference is accelerated.

Thats why,;

Earth is considered as a non inertial frame of reference.

What do you think, is it easy for you to understand this concept of inertial frame of reference?

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Inertial Frame Of Reference Examples

Here are the Real Life examples of inertial frame of reference:

  • A frame of reference of a bus
  • A frame of reference of a ship
  • A frame of reference of a bicycle
  • A frame of reference of a cable car
  • A frame of reference of a missile

Any object whose frame of reference is either at rest or moving with constant velocity is in an inertial frame of reference.

You might be thinking, HOW?

Lets understand the above examples in detail.

Inertial Frame Of Reference :

Any frame of reference in which Newtons Ist law is observed to hold is inertial i.e. a body on which no net force is acting moves with constant velocity with respect to this frame.All frames of reference moving with constant velocity w.r.t. any inertial frame of reference are also inertial.

Any two inertial frames of reference move with constant velocity relative to each other.

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Inertial Frame Of Reference Definition

In physics, the definition of inertial frame of reference can be stated as:

A frame of reference which is at rest or moving with constant velocity is known as inertial frame of reference

In simple terms,

A frame of reference which is not accelerated is known as the inertial frame of reference.

You might have not understood the above statement properly.

Dont worry !!

Lets consider some real life examples to understand the above definition of inertial frame of reference.

So youll get a clear idea.

First Postulate Of Special Relativity

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The laws of physics are the same and can be stated in their simplest form in all inertial frames of reference.

As with many fundamental statements, there is more to this postulate than meets the eye. The laws of physics include only those that satisfy this postulate. We shall find that the definitions of relativistic momentum and energy must be altered to fit. Another outcome of this postulate is the famous equation E;=;mc2.

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What Are Frames Of Reference

Velocity, acceleration, and displacement have all been discussed. All of these numbers, however, to measure all of the above-mentioned parameters in a practical use case scenario, requires a frame of reference against which they can be measured.

A frame of reference in physics is made up of an abstract coordinate system and a collection of physical reference points that then later establishes the coordinate system and standardizes measurements inside it.

Non Inertial Frame Of Reference

The definition of non inertial frame of reference can be stated as:

A frame of reference which is not moving with constant velocity or is accelerated is known as non inertial frame of reference

In simple words,;

When a frame of reference is accelerated, it is known as the non inertial frame of reference.

Lets consider a similar example of a bike as discussed above.

But in this case, a bike is accelerated.

Now the question is,;

Is a bike in the inertial or non inertial frame of reference?

Lets find out.

When a bike is accelerated, the frame of reference of a bike also gets accelerated.

So, a bike is said to be in the non inertial frame of reference.

Now,

Why is Newtons first law invalid in the non inertial frame of reference?

The reason is simple.

Look, when a bike is accelerated, a bike is not at rest or moving with constant velocity, right?

And you know that Newtons first law is valid only when an object is at rest or moving with constant velocity.

Thats why Newtons first law is invalid in the non inertial frame of reference.

In short,;

When a bike is accelerated forward, the frame of reference of a bike also gets accelerated.

So, a bike is said to be in the non inertial frame of reference.

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From Special Relativity And Lorentz Invariance To General Relativity And General Covariance

It may seem surprising that, after this insightful analysis of theconcept of inertial frame and its role in electrodynamics, Einsteinshould have turned almost immediately to call that concept intoquestion. But he became convinced, largely by his reading of Mach,that the central role of inertial frames was an epistemologicaldefect that special relativity shared with Newtonian mechanics.Only relative motions are observable, yet both of these theoriespurport to identify a privileged state of motion and use it to explainobservable effects . Coordinate systemsare not observable, yet both of these theories assign a fundamentalphysical role to certain kinds of coordinate system, namely, theinertial systems. In either theory, inertial coordinates aredistinguished from all others, and the laws of physics are said tohold only relative to inertial coordinate systems. In anepistemologically sophisticated theory, both of these problems wouldbe solved at once: the new theory would only refer to what isobservable, which is relative motion; it would admit arbitrarycoordinate systems, instead of confining itself to a special class ofsystem. Why, after all, should any genuine physical phenomenon dependon the choice of coordinate system?

Inertial Frames Of Reference

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An inertial frame of reference is one in which Newtons Laws of motion are valid. It is a non-accelerated frame of reference. An inertial frame must be homogeneous and isotropic. Physical experiments can be carried out in different inertial reference frames. The Galilean transformation provides a means of converting between two inertial frames of reference moving at a constant relative velocity. Consider two reference frames \ and \ with \ moving with constant relative velocity \ at time \. Figure \ shows a Galilean transformation which can be expressed in vector form.

\begin \begin \mathbf & =\mathbf-\mathbft \\ t’ & = t \end\label\end

Equation \ref gives the boost, assuming Newtons hypothesis that the time is invariant to change of inertial frames of reference. Differentiation of this transformation gives

\begin\mathbf’} & =\mathbf}-\mathbf\\\mathbf’} & = \mathbf}\end\label\end

Note that the forces in the primed and unprimed inertial frames are related by \begin\label\mathbf=\frac}=m\mathbf}=m\mathbf’}=\mathbf’\end

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