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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 deduct five minutes from the time displayed on your watch in order to obtain the correct time.
For a simple example involving only the orientation of two observers, consider two people standing, facing each other on either side of a north-south street.
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 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. 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.
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 in the negative x -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 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 the 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 and 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.
This concept of time and simultaneity was later generalized by Einstein in his special theory of relativity where he developed transformations between inertial frames of reference based upon the universal nature of physical laws and their economy of expression Lorentz transformations.
It is also important to note that the definition of inertial reference frame can be extended beyond three-dimensional Euclidean space.
As an example of why this is important, let us consider the geometry of an ellipsoid. In this geometry, a "free" particle is defined as one at rest or traveling at constant speed on a geodesic path.
Two free particles may begin at the same point on the surface, traveling with the same constant speed in different directions.
After a length of time, the two particles collide at the opposite side of the ellipsoid. Both "free" particles traveled with a constant speed, satisfying the definition that no forces were acting.
This means that the particles were in inertial frames of reference. Since no forces were acting, it was the geometry of the situation which caused the two particles to meet each other again.
In a similar way, it is now common to describe  that we exist in a four-dimensional geometry known as spacetime. In this picture, the curvature of this 4D space is responsible for the way in which two bodies with mass are drawn together even if no forces are acting.
This curvature of spacetime replaces the force known as gravity in Newtonian mechanics and special relativity. Here the relation between inertial and non-inertial observational frames of reference is considered.
The basic difference between these frames is the need in non-inertial frames for fictitious forces, as described below.
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.
From the geometry of the situation, we get. When there is accelerated motion due to a force being exerted there is manifestation of inertia.
If an electric car designed to recharge its battery system when decelerating is switched to braking, the batteries are recharged, illustrating the physical strength of manifestation of inertia.
However, the manifestation of inertia does not prevent acceleration or deceleration , for manifestation of inertia occurs in response to change in velocity due to a force.
A common sort of accelerated reference frame is a frame that is both rotating and translating an example is a frame of reference attached to a CD which is playing while the player is carried.
This arrangement leads to the equation see Fictitious force for a derivation:. From Wikipedia, the free encyclopedia. Not to be confused with Inertial frame of reference.
For other uses, see Frame of reference disambiguation. Second law of motion. Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational speed.
Generalized coordinates and Axes conventions. Inertial frame of reference. This section does not cite any sources. Please help improve this section by adding citations to reliable sources.
Unsourced material may be challenged and removed. July Learn how and when to remove this template message. Special theory of relativity and General theory of relativity.
Fictitious force , Non-inertial frame , and Rotating frame of reference. See, for example, Kurt Edmund Oughstun Electromagnetic and Optical Pulse Propagation 1: Spectral Representations in Temporally Dispersive Media.
These distinctions also appear in thermodynamics. See Paul McEvoy Topological Groups 3rd ed. As such, the coordinate system is a mathematical construct, a language, that may be related to motion, but has no necessary connection to motion.
Handbook of Continuum Mechanics: Essays on the Formal Aspects of Electromagnetic Theory. Metaphysical essays on space and time.
General covariance and the foundations of general relativity: Analytical Mechanics for Relativity and Quantum Mechanics. Classical dynamics Reprint of edition by Prentice-Hall ed.
Classical Relativistic Many-Body Dynamics. Theoretical Physics Reprint of the 2nd ed. Introduction to Hyperbolic Geometry. This structure allows differentiation to be defined, but does not distinguish between different coordinate systems.
Thus, the only concepts defined by the manifold structure are those that are independent of the choice of a coordinate system.
Hawking; George Francis Rayner Ellis A mathematical definition is: A connected Hausdorff space M is called an n -dimensional manifold if each point of M is contained in an open set that is homeomorphic to an open set in Euclidean n -dimensional space.
Geometry of Differential Forms. American Mathematical Society Bookstore. Mathematical handbook for scientists and engineers: Simulating and Generating Motions of Human Figures.
Lectures on General Relativity. Dynamics of the Atmosphere. Vector and Tensor Analysis with Applications. How and Why in Basic Mechanics.
The term may also be used more generally as a noun or verb to refer to the edges of the image as seen in a camera viewfinder or projected on a screen.
Thus, the camera operator can be said to keep a car in frame by panning with it as it speeds past. Persistence of vision blends the frames together, producing the illusion of a moving image.
The frame is also sometimes used as a unit of time, so that a momentary event might be said to last six frames, the actual duration of which depends on the frame rate of the system, which varies according to the video or film standard in use.
In North America and Japan, 30 frames per s: In a strip of movie film, individual frames are separated by frame lines. Normally, 24 frames are needed for one second of film.
In ordinary filming, the frames are photographed automatically, one after the other, in a movie camera. In special effects or animation filming, the frames are often shot one at a time.
The size of a film frame varies, depending on the still film format or the motion picture film format. In the smallest 8 mm amateur format for motion pictures film, it is only about 4.
The larger the frame size is in relation to the size of the projection screen , the sharper the image will appear.
The size of the film frame of motion picture film also depends on the location of the holes, the size of the holes, the shape of the holes.
A system called KeyKode is often used to identify specific physical film frames in a production. Historically, video frames were represented as analog waveforms in which varying voltages represented the intensity of light in an analog raster scan across the screen.
Analog blanking intervals separated video frames in the same way that frame lines did in film. For historical reasons, most systems used an interlaced scan system in which the frame typically consisted of two video fields sampled over two slightly different periods of time.
This meant that a single video frame was usually not a good still picture of the scene, unless the scene being shot was completely still.
Standards for the digital video frame raster include Rec. The frame is composed of picture elements just like a chess board. Each horizontal set of picture elements is known as a line.
The picture elements in a line are transmitted as sine signals where a pair of dots, one dark and one light can be represented by a single sine.
The product of the number of lines and the number of maximum sine signals per line is known as the total resolution of the frame.
The higher the resolution the more faithful the displayed image is to the original image. But higher resolution introduces technical problems and extra cost.
So a compromise should be reached in system designs both for satisfactory image quality and affordable price.
The key parameter to determine the lowest resolution still satisfactory to viewers is the viewing distance, i.
The total resolution is inversely proportional to the square of the distance. If d is the distance, r is the required minimum resolution and k is the proportionality constant which depends on the size of the monitor;.
Since the number of lines is approximately proportional to the resolution per line, the above relation can also be written as.
That means that the required resolution is proportional to the height of the monitor and inversely proportional to the viewing distance.
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