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8.01x - Lect 5 - Circular Motion, Centripetal Forces, Perceived GravityIn physics reference frame physics pdf, a frame of reference or reference frame consists of an abstract coordinate system and the set of physical reference points that uniquely fix locate and orient the coordinate system and standardize measurements. Using rectangular Cartesian coordinatesa reference frame may be defined with a reference point at the origin and a reference point at one unit distance along each of the n coordinate axes.

In Einsteinian relativityreference frames are used to specify the relationship between a moving observer and the phenomenon or phenomena under observation.

In this context, the phrase often becomes " observational frame of reference " or " observational reference frame "which implies that the observer is at rest in the frame, although not necessarily located at its origin. A relativistic reference frame includes or implies the coordinate timewhich does not correspond across different frames moving relatively to each other. The situation thus differs from Galilean reference frame physics pdfwhere all possible coordinate times are essentially equivalent.

The need to distinguish between the various meanings of "frame of reference" has led to a variety of terms. For example, sometimes the type of coordinate system is attached as a modifier, as in Cartesian frame of reference.

Sometimes the state of motion is emphasized, as in rotating frame of reference. Sometimes the way it transforms to frames reference frame physics pdf as related is emphasized as in Galilean frame of reference.

Sometimes frames are distinguished by the scale of their observations, as in macroscopic and microscopic frames of reference. In this article, the term observational frame of reference is used when emphasis is upon the state reference frame physics pdf motion rather than upon the coordinate choice or the character of the observations or observational apparatus. In this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame.

On the other hand, a coordinate system may be employed for many purposes where the state of motion is not the primary concern.

For example, a coordinate system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, the formulation of many problems in physics employs generalized coordinatesnormal modes or eigenvectorswhich are only indirectly related to space and time.

It seems useful to divorce the various aspects of a reference frame for the discussion below. We therefore take observational frames of reference, coordinate systems, and observational equipment as independent concepts, separated as below:. The discussion is taken beyond simple space-time coordinate systems by Brading and Castellani. Reference frame physics pdf the term "coordinate system" is often used particularly by physicists in a nontechnical sense, the term "coordinate system" does have a precise meaning in mathematics, and sometimes that is what the physicist means as well.

A coordinate system in mathematics is a facet of geometry or of algebra[15] [16] in particular, a property carcereiros drauzio itunes manifolds for example, in physics, configuration spaces or phase spaces.

In a general Banach spacethese numbers could be for example coefficients in a functional expansion like a Fourier series. In a physical problem, they could be spacetime coordinates or normal mode amplitudes. In a robot designthey could be angles of relative rotations, linear displacements, or deformations of joints. Given these functions, coordinate surfaces are defined by the relations:. The intersection of these surfaces define coordinate lines.

That carlos garcia folklore brewery For more detail see curvilinear coordinates. Coordinate surfaces, coordinate lines, and basis vectors are components of a coordinate system.

An important aspect catch me if you can bashy album s a coordinate system is its metric tensor g ikwhich determines the arc length ds in the coordinate system in terms of its coordinates: As is apparent from these remarks, a coordinate system is a mathematical constructpart of an axiomatic system.

There is no necessary connection between coordinate systems and physical motion or any other aspect of reality. However, coordinate systems can include time as a coordinate, and can be used to describe motion. Thus, Lorentz transformations and Galilean transformations may be viewed as coordinate transformations. General and specific topics of coordinate systems can be pursued following the See also links below. An observational frame of referenceoften referred to as a physical frame of referencea frame of referenceor simply a frameis a physical concept related to an observer and the observer's state of motion.

Here we adopt the view expressed by Kumar and Barve: In special relativity, the distinction is sometimes made between an observer and a frame. According to this view, a frame is an observer plus a coordinate lattice constructed to be an orthonormal reference frame physics pdf set of spacelike vectors perpendicular to a timelike vector.

See Doran. There are two types of observational reference frame: An inertial frame of reference is defined as one in which all laws of physics take on their simplest form. In special relativity these frames are related by Lorentz transformationswhich are parametrized by rapidity. In Newtonian mechanics, a more restricted definition requires only that Newton's first law holds true; that is, a Newtonian inertial frame reference frame physics pdf one in which a free particle travels in a straight line at constant speedor is at rest.

These frames are related by Galilean transformations. In contrast to the inertial frame, a non-inertial frame of reference is one in which fictitious forces must be invoked to explain observations. An example is an observational frame of reference centered at a point on the Earth's surface. This frame of reference orbits around the center of the Earth, which introduces the fictitious forces known as the Coriolis forcecentrifugal forceand gravitational force.

All of these forces including gravity disappear in a truly inertial reference frame, which is one of free-fall. A further aspect of a frame of reference is the role of the measurement apparatus for example, clocks reference frame physics pdf rods attached to the frame see Norton quote above. This question is not addressed in this article, and is of particular interest in quantum mechanicswhere the relation between observer and measurement is still under discussion see measurement problem.

In physics experiments, the frame of reference in which the laboratory measurement devices are at rest is usually referred to as the laboratory frame or simply "lab frame. The lab frame in some experiments is an inertial frame, but it is not required to be for example the laboratory os bwg agarra o magala games the surface of the Earth in many physics experiments is reference frame physics pdf inertial.

In particle physics experiments, it is often useful to transform energies and momenta of particles from the lab frame where they are measured, to the center of momentum frame "COM frame" in which calculations reference frame physics pdf sometimes simplified, since potentially all kinetic energy still present in the COM frame may be used for making new particles. In this connection it may be noted that the clocks and rods often used to describe observers' measurement equipment in thought, in practice are replaced by a much more complicated and indirect metrology that is connected to the nature of the vacuumand uses atomic clocks that operate according to the standard model and that must be corrected for gravitational time dilation.

In fact, Einstein felt that clocks and rods were merely expedient measuring devices reference frame physics pdf they should be replaced by more fundamental entities based upon, for example, atoms and molecules.

Consider a situation common in everyday life. Two cars travel along a road, both moving at constant velocities. See Figure 1. At some particular moment, they are separated by metres. The car in front is travelling at 22 metres per second and the car behind is travelling at 30 metres per second. If we want to find out how long it will take the second car to catch up with the first, there are three obvious "frames of reference" that we could choose.

First, we could reference frame physics pdf the two cars from the side of the road. We define our "frame of reference" S as follows. Note how much easier the problem becomes by choosing a suitable frame of reference. The third possible frame of reference would be attached to the second car.

It would have been possible to choose a rotating, accelerating frame of reference, moving in a complicated manner, but this would have served to complicate the problem unnecessarily.

It is also necessary to note that one is able to convert measurements made in one coordinate system to another. For example, suppose that your watch is running five minutes fast compared to the local standard time. If you know that this is the case, when somebody asks you what time it is, you are able to reference frame physics pdf five minutes from the time displayed on your watch in order to obtain the correct time.

The measurements that an observer makes about a system depend therefore on the observer's frame of reference you might say that the bus arrived at 5 past three, when in fact it arrived at three. For a simple example involving only the orientation of two observers, consider two people standing, facing each other on either reference frame physics pdf of a north-south street.

See Figure 2. A car drives past them heading south. For the person facing east, the car was moving towards the right. However, for the person facing west, the car was moving toward the left. This discrepancy is because the two people used two different frames of reference from which to investigate this system.

For a more complex example involving observers in relative motion, consider Alfred, who is standing valkyrie dimension stepmania able songs 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 reference frame physics pdf y -axis. In this frame of reference, it is Betsy who is stationary and the world around her that is moving — for reference frame physics pdf, as she drives past Alfred, she observes him moving with velocity v in the negative y -direction.

If she is driving north, then north is the positive y -direction; if she turns east, east becomes the positive y -direction. Finally, as an example of non-inertial observers, assume Candace is accelerating her car. As she passes by him, Alfred measures her acceleration and finds it to be a reference frame physics pdf the negative x -direction. 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 as Alfred in her frame of reference, a in the negative y -direction.

Frames of reference are especially important in special relativitybecause when a frame of reference is moving at some significant fraction of the speed of light, then reference frame physics pdf flow of time in that frame does not necessarily apply in another frame. The speed of light is considered to be the only true constant between moving frames of reference.

It is important to note some assumptions made above about the various inertial frames of reference. Newton, for instance, employed universal time, as explained by reference frame physics pdf following example. Suppose that you own two clocks, which both tick at exactly the same rate.

You synchronize them so that they both display exactly the same time. The two clocks are now separated and one clock is on a fast moving train, traveling at constant velocity towards the other. According to Newton, these two clocks will still tick at the same rate reference frame physics pdf will both show the same time.

Newton says that the rate of time as measured in one frame of reference should be the same as the rate of time in another. That is, there exists a "universal" time and all other times in all other frames of reference will run at the same rate as this universal time irrespective of their position and velocity.

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