In special relativity, time becomes a coodinate on a nearly equal footing with the space coordinates. The primary rigid reference frames are the inertial reference frames , which can be mapped to each other via the Lorentz transformations. The Lorentz transformations again include displacement and velocity, but rotation is not as cleanly separated any more. If one applies an "x-boost" transformation changing the velocities in the x direction, and next a y-boost, one finds that the final coordinate axes are not parallel to the original ones.

This non-commutivity leads to the Thomas precession. The principle of relativity states that, even though a set of measurements may depend on an observer's particular frame of reference, the observed physical events still must follow the same physical laws in all inertial frames of reference.

## Frame of reference

For example, consider Alfred, who is standing on the side of a road watching a car drive past him from left to right. In his frame of reference, Alfred defines the spot where he is standing as the origin, the road as the x-axis and the direction in front of him as the positive y-axis. To him, the car moves along the x axis with some velocity v in the positive x-direction.

Alfred's frame of reference is considered an inertial frame of reference because he is not accelerating ignoring effects such as Earth's rotation and gravity. Now consider Betsy, the person driving the car.

Betsy, in choosing her frame of reference, defines her location as the origin, the direction to her right as the positive x-axis, and the direction in front of her as the positive y-axis. In this frame of reference, it is Betsy who is stationary and the world around her that is moving - for instance, as she drives past Alfred, she observes him moving with velocity v in the negative y-direction.

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If she is driving north, then north is the positive y-direction; if she turns east, east becomes the positive y-direction. Now assume Candace is driving her car in the opposite direction. As she passes by him, Alfred measures her acceleration and finds it to be a in the negative x-direction.

### Introduction

Assuming Candace's acceleration is constant, what acceleration does Betsy measure? If Betsy's velocity v is constant, she is in an inertial frame of reference, and she will find the acceleration to be the same - in her frame of reference, a in the negative y-direction. Frames of reference are especially important in special relativity , because when a frame of reference is moving at some significant fraction of the speed of light, then the flow of time in that frame does not necessarily apply in another reference frame.

The speed of light is considered to be the only true constant between moving frames of reference. When working a problem involving one or more frames of reference it is common to designate an inertial frame of reference.

### frame of reference

An accelerated frame of reference is often delineated as being the "primed" frame, and all variables that are dependent on that frame are notated with primes, e. The vector from the origin of an inertial reference frame to the origin of an accelerated reference frame is commonly notated as R.

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Given a point of interest that exists in both frames, the vector from the inertial origin to the point is called r , and the vector from the accelerated origin to the point is called r'. From the geometry of the situation, we get.

These equations allow transformations between the two coordinate systems; for example, we can now write Newton's second law as. This force we call as pseudo force. Now, we can work on a problem from an accelerated reference frame by just adding a pseudo force and pretending that nothing has changed. A frame of reference either at rest or moving with a uniform velocity zero acceleration is known as inertial frame. All the laws of physics hold good in such a frame. It is a frame of reference which is either having a uniform linear acceleration or is being rotated with uniform speed.

An inertial frame is endowed with the following characteristics:. Is earth an inertial frame of reference? Earth rotates around its axis as also revolves around the sun. In both these motion, centripetal acceleration is present. Therefore, strictly speaking earth or any frame of reference fixed on earth cannot be taken as an inertial fame. Furthermore, this speed of earth can be assumed to be constant. Hence earth or any other frame of reference set up on earth can be taken as an approximately inertial frame of reference.

On the contrary, a frame of reference which is accelerated or decelerated is a non-inertial frame. Apparent weight of a man inside a lift Suppose that you are standing on the balcony of a tall tower, facing east. You drop an object so that it falls to the ground below; see below figure. Suppose also that you can locate the impact point very precisely. Will the object strike the ground at a, vertically below the release point, at b to the east, or at c to the west?

The object was released from rest; the Earth rotates from west to east. In case the factor is non-negligible, and the Earth moves from West to East, the object will hit the ground at point c. The situation is similar to the perceived leftward displacement of the air moving to a low pressure point from north to south. To the person standing on the balcony of a tall tower, a psuedo force has acted on the object in a direction from east to west.

What is the distinction between inertial reference frames and those differing only by a translation or rotation of the axes? One can distinguish the inertial frame of reference against the translation of the axes when the translation or rotation occurs non-uniformly. If the translation of one frame of reference relative to the other is such that observer in one frame measures some acceleration of the other, then the observer can draw a distinction between his frame and the inertial frame of reference.

It is important to note that the rotating frame will always be non-inertial because to account for the rotation there must be a change in velocity vector. Therefore the inertial reference frame will always be distinct from the rotation frame. However the translation can be distinguished from the inertial frame of reference only when the translation occurs at a uniform velocity. A passenger in the front seat of a car finds himself sliding toward the door as the driver makes a sudden left turn. Describe the forces on the passenger and on the car at this instant if the motion is viewed from a reference frame a attached to the Earth and b attached to the car.

This causes the passenger to move in the direction of velocity vector of car before car took a turn.

Therefore, to the observer at Earth frame, the passenger has the initial velocity equal to the velocity of the car before it takes the turn. The observer also see the car taking a turn, and accounts for an acceleration for the same. Thus, the observer would expect frictional forces to exist between the passenger and the seat.

Given that the passenger has moved towards the door when the car took a left turn, it is obvious that the passenger moves to the right. Therefore the frictional force would be in a direction opposite to the motion of the passenger, that is, towards the left. Therefore the magnitude of frictional force between the passenger and the seat is equal to the magnitude of the deceleration of the passenger.

Therefore a psuedo force will act on the passenger, accelerating him in the direction of the seat. But there is a friction between the seat of the car and the passenger, which decelerate the passenger in a direction opposite to the direction of its motion. Thus the magnitude of net force acting on the passenger is the difference between magnitude the centrifugal force and magnitude the frictional force.

Therefore one can see that the perceived acceleration for the observer in car differs from that of the observer on Earth. If not, why not? No, one does not have to concern with the Carioles Effect when playing tennis or golf because the factor by which the Earth rotates during the time the ball goes from its source to the destination, is very small and can be neglected.

Which of the following will not depend on orientation of frame of reference:. A boy sitting in a moving train throws a ball straight up into the air. The ball falls behind him. So the train is. You might like to refer Momentum. To read more, Buy study material of Laws of Motion comprising study notes, revision notes, video lectures, previous year solved questions etc.

## frame of reference - Wiktionary

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