Physics
Frame of Reference
A frame of reference in physics is a coordinate system used to describe the position, orientation, and motion of objects. It provides a point of view from which measurements and observations are made. Different frames of reference can yield different descriptions of the same event, highlighting the importance of choosing an appropriate frame for analyzing physical phenomena.
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8 Key excerpts on "Frame of Reference"
eBook - PDF- Wolfgang Torge, Jürgen Müller(Authors)
- 2012(Publication Date)
- De Gruyter(Publisher)
2 Reference Systems and Reference Frames Reference systems are required in order to describe the position and motion of the Earth and other celestial bodies including artificial satellites, positions and movements on the surface of the Earth, and the stationary and time-variable parts of the Earth’s gravity field. They are represented by coordinate systems , which – in Newtonian space – are three-dimensional in principle, and defined with respect to origin, orientation, and scale. A fourth dimension, time, enters through the mutual motion of the Earth and other celes-tial bodies and through the temporal variations of the Earth’s shape, its gravity field and its orientation. Present-day measurement accuracy even requires a four-dimensional treatment in the framework of general relativity, with rigorous coupling of space and time. Reference systems are realized through reference frames consisting of a set of well-determined fixed points or objects, given by their coordinates and (if necessary) velocities at a certain epoch. They serve for modeling geodetic observations, as a func-tion of a multitude of geometric and physical parameters of interest in geodesy and other geosciences. Basic units and constants are fundamental to the geodetic measurement and model-ing processes [2.1]. Time systems are based either on processes of quantum physics, on motions in the solar system, or on the daily rotation of the Earth [2.2]. The geometric properties of reference systems are provided by three-dimensional coordinates, here we distinguish between a space-fixed celestial and an Earth-fixed terrestrial reference system [2.3]. Conventional reference systems and corresponding reference frames are provided by the International Earth Rotation and Reference Systems Service IERS [2.4]. In addition, gravity field-related local level systems have to be introduced, as most geo-detic observations refer to gravity [2.5].
eBook - PDF- David Agmon, Paul Gluck;;;(Authors)
- 2009(Publication Date)
- WSPC(Publisher)
Chapter 3 Relative Motion and Frames of Reference Do not judge your fellow man until you are in his place. Sayings of the Fathers 3.1 Introduction Relative velocity and even more, relative acceleration are topics usually neglected in introductory textbooks. This is unfortunate, as the equivalence of all inertial frames of reference is a basic tenet in modern physics, and has also been generalized to accelerated, non-inertial systems. It is also of great importance to the learner to be able to tackle problems from different points of view, often leading him to surprisingly simple solutions and insights. The flexibility of thought induced by the maxim what you see from here may not be what you see from there is of considerable importance. At one time space was believed to be permeated by a mysterious substance called the ether. It was supposed to be at absolute rest and therefore to serve as an absolute Frame of Reference relative to which all motion could be measured. The famous experiment of Michelson and Morley (1896) disposed of the ether once and for all, and with it went the ability to distinguish between a state of rest and one of uniform motion with constant velocity. This led to the following important conclusions: (a) There is no such thing as absolute velocity, the velocity of any body is relative (to some Frame of Reference). (b) All observers moving relative to each other with constant velocity are equivalent. Every observer can argue that he is at rest and that bodies moving with respect to him are in motion. In the sequel this principle of equivalence will be generalized to accelerated systems. Equivalence is not meant to imply that different observers will describe the same event in an identical manner. Clearly, the trajectory of a moving body will look different in different reference frames. Equivalence requires that the functional form of physical laws relating dynamical variables will be identical in all inertial frames.
eBook - PDF- Mohhamad Reza Kiani(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
Let us sum up: A Frame of Reference does not constitute a piece of unreal geometry anymore; it is a heavy laboratory, built on a rigid body of tremendous mass, as compared to masses in motion. Insufficient masses yield incomplete steadfastness—Here appear the effects of tides, with easily visiole action and reaction. 46 COORDINATES AND FRAMES We will be told: You are discovering the moon! No! We are only discovering that the moon should not be ignored in one chapter and correctly mentioned in another. The use of accelerated frames of reference strengthens our arguments. What is the meaning of a frame S 2 in uniform rotation with respect to a motionless frame S x ? To give it a physical mean-ing, we have to see it as a very heavy wheel, a flywheel of high inertia, which carries away together the observer and the moving instrument under observation (both very light). If this condition is not fulfilled, any displacement of a mass m within the rotating frame modifies the moment of inertia of this frame and provokes a change in the speed of rotation . The flywheel must have an infinite .moment of inertia so that we can consider ω as a constant when the observer and the moving instrument are arbitrarily dis-placed. The action (upon the moving instrument) is equal to the reaction (upon the Frame of Reference). The effect of this reaction can be ignored only if the mass of the frame is infinite. These conditions are, moreover, realized in a laboratory on earth. The situation in an accelerated Frame of Reference is about the same as that observed in gravitation. A weighty object, ob-served on the earth, is placed into a field of gravitation which is in superposition with the effects of rotation. The action (upon the apple of Newton or upon our projectile) is equal to the reaction on earth. 4. Actions and Reactions in Relativity In classical mechanics, all these effects are supposed to be trans-mitted instantaneously at any distance.
eBook - PDFThe Sciences
An Integrated Approach
- James Trefil, Robert M. Hazen(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
In each of these reference frames you are what scientists call an “observer.” An observer looks at the world from a particular Frame of Reference with anything from casual interest to a full-fledged laboratory investigation of phenomena that leads to a determination of natural laws. For human beings who grow up on Earth’s surface, it is natural to think of the ground as a fixed, immovable Frame of Reference and to refer all motion to it. After all, train or plane passengers don’t think of themselves as stationary while the countryside zooms by. But, as we saw in the opening example, there are indeed times when we lose this preju- dice and see that the question of who is moving and who is standing still is largely one of definition. From the point of view of an observer in a spaceship above the solar system, there is nothing “solid” about the ground you’re standing on. Earth is rotating on its axis and moving in an orbit around the Sun, while the Sun itself is performing a stately rotation around the galaxy. Thus, even though a reference frame fixed in Earth may seem “right” to us, there is nothing special about it. Waiting at the Stoplight Waiting in your car at a long stoplight, you daydream about the friends you’re going to meet. You don’t even notice the large bus in the lane next to you. Suddenly you have the strange sensation that your car is moving backward. But your foot is on the brake—how can that be? You quickly realize that it’s the bus that’s moving forward, not you moving backward. It was just a brief optical illusion. For that brief moment you saw the world through eyes unaffected by years of experi- ence. You realized that there is always more than one way to view any kind of motion. One way, of course, is to say that you are stationary and the bus is moving with respect to you. But you could also say that the bus is stationary and you are moving backward relative to it.
eBook - PDFScience and Theology
Questions at the Interface
- Murray Rae, Hilary Regan, John Stenhouse(Authors)
- 2016(Publication Date)
- Bloomsbury Academic(Publisher)
This position has been severely questioned and is regarded by many as indefensible because one's perception of reality is determined by one's Frame of Reference, and all frames of reference are relative. This, however, is a misunderstanding. If a scientist, acknowledging the particularity of his Frame of Reference, accepting without question that he cannot expect to go out of his frame to see reality in its totality, insists nevertheless that the ruler and the clock in his frame are absolute standards for him because they are the only standards he knows and uses; and if, further, he then seeks to describe physical events and understand the order in them as 196 Carver TYu faithfully and intelligently as he can, then he would indeed be condemned to the narrow confines of his frame, and the structure of the reality that he sees would be confined to what his frame allows him to see. He would never be able to rise above the fragmentary nature of his particular view to a total view of the natural process. He would not be able to see that the space his ruler measures and the time his clock records, relative as they may be, can be correlated in such a way as to arrive at a space-time interval which is the same for all observers in various frames for each and every event. And as he strives to get a broader picture of reality, he will bump into a wall of paradoxes. Such a picture is absurd. No scientist thinks this way. Acknow-ledging the relativity of each frame in the description of physical events for the unravelling of order therein, scientists nevertheless seek to transcend the confines of each and every frame to get to a total picture of reality, thus enabling them to envisage what reality would be like in the particularity of each frame. In so doing, they acknowledge that the measuring standards (measuring rod and clock) good for measuring things within their own frames are not enough for a wider horizon of reality.
eBook - PDF- David H. Eberly(Author)
- 2010(Publication Date)
- CRC Press(Publisher)
The equations of motion F = ma will be used to establish the path of motion for an object by numerically solving the second-order differential equations for position. Each of the vector quantities of position, velocity, and acceleration is measured with respect to some coordinate system. This system is referred to as the inertial frame. If x = (x 1 , x 2 , x 3 ) is the representation of the position in the inertial frame, the components x 1 , x 2 , and x 3 are referred to as the inertial coordinates. Although in many cases the inertial frame is considered to be fixed (relative to the stars as it were), the frame can have a constant linear velocity and no rotation and still be inertial. Any other Frame of Reference is referred to as a noninertial frame. In many situations it is important to know whether the coordinate system you use is inertial or noninertial. In particular, we will see later that kinetic energy must be measured in an inertial system. 2.4 Forces A few general categories of forces are described here. We restrict our attention to those forces that are used in the examples that occur throughout this book. For example, we are not going to discuss forces associated with electromagnetic fields. 32 Chapter 2 Basic Concepts from Physics 2.4.1 Gravitational Forces Given two point masses m and M that have gravitational interaction, they attract each other with forces of equal magnitude but opposite direction, as indicated by Newton’s third law. The common magnitude of the forces is F gravity = GmM r 2 (2.46) where r is the distance between the points and G . = 6.67 × 10 −11 newton-meters squared per kilogram squared. The units of G are selected, of course, so that F gravity has units of newtons. The constant is empirically measured and is called the universal gravitational constant.
- Andrei D. Polyanin, Alexei Chernoutsan(Authors)
- 2010(Publication Date)
- CRC Press(Publisher)
Chapter P1 Physical Foundations of Mechanics Preliminary remarks. Mechanical motion is change in the location of a body with respect to other bodies. This definition implies that mechanical motion is relative. In order to describe motion, one should specify a Frame of Reference , which includes a body of reference, a coordinate system fixed relative to the body, and a set of clocks synchronized with one another. Mechanics studies motions of model objects, a point particle (or a point mass) and a rigid body. The location of these objects is determined by a finite set of independent parameters; the objects are said to have finitely many degrees of freedom . Kinematics deals with the characterization of motion without finding out its reasons. P1.1. Kinematics of a Point P1.1.1. Basic Definitions. Velocity and Acceleration ◮ Point particle. Law of motion. Path, distance and displacement. A body whose dimensions can be neglected in studying its motion (compared to the distances of its movement) is called a point particle (or just a particle ). The position of a point particle at an instant of time t is determined by the position vector r from the origin of some reference frame to the particle (see Fig. P1.1). As the particle moves, the end of the position vector traces a spatial curve, a path (also called a trajectory ). In a rectangular Cartesian reference frame, the position vector is determined by its projections onto the coordinate axis, its x -, y -, and z -coordinates. The motion of a particle is completely determined by specifying its law of motion , a single vector function r ( t ) or three scalar functions x ( t ), y ( t ), z ( t ). A position vector (or any other vector) can be conveniently written in terms of its projections using unit vectors, i , j , and k , of the respective coordinate axes as follows: r = x i + y j + z k . The distance traveled by the particle in a given time interval is measured along the curvilinear path.
eBook - PDFThe Mechanical Universe
Mechanics and Heat, Advanced Edition
- Steven C. Frautschi, Richard P. Olenick, Tom M. Apostol, David L. Goodstein(Authors)
- 2008(Publication Date)
- Cambridge University Press(Publisher)
CHAPTER FORCES IN ACCELERATING REFERENCE FRAMES From the beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer [moving relative to the earth], everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. Albert Einstein. Autobiographical Notes (1949) 9.1 INERTIAL AND NONINERTIAL REFERENCE FRAMES We have already introduced Galileo's ideas on relative motion in Chapter 4 . We defined inertial frames - frames in which the law of inertia holds - and remarked that an observer in any inertial frame deduces the same laws of motion, and has no way of determining whether he is at rest or moving in an absolute sense, Galileo was able to provide striking examples of these ideas, such as a stone dropped from the mast of a moving boat, and 203 204 FORCES IN ACCELERATING REFERENCE FRAMES to deduce a vitally important application - the earth need not be considered the stationary hub around which the heavens revolve. However, Galileo did not have a clear-cut dynamical framework within which to derive his ideas. And exactly how to treat motion in a rotating frame, or indeed in any noninertial frame - one that is accelerated relative to an inertial frame - remained obscure. It was only after Newton's second law was discovered that Galileo's ideas could be derived in a clear-cut way. Moreover, Newton's laws could be used in accelerated as well as inertial frames. This allowed Newton to supplement his description of circular motion as viewed from an inertial frame (where, as we have seen, some physical force must supply a centripetal acceleration) with a treatment of circular motion as felt by an observer riding along with the circling object.
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