# 1.1 Coordinate systems in physics

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Coordinate system is a mathematical construct to measure distance and direction in relation to a system of rigid bodies. The connection to rigid bodies is a crucial consideration for drawing a coordinate system, with out which coordinate system has no meaning in physics.

Coordinate system is a system of measurement of distance and direction with respect to rigid bodies. Structurally, it comprises of coordinates and a reference point, usually the origin of the coordinate system. The coordinates primarily serve the purpose of reference for the direction of motion, while origin serves the purpose of reference for the magnitude of motion.

Measurements of magnitude and direction allow us to locate a position of a point in terms of measurable quantities like linear distances or angles or their combinations. With these measurements, it is possible to locate a point in the spatial extent of the coordinate system. The point may lie anywhere in the spatial (volumetric) extent defined by the rectangular axes as shown in the figure. (Note : The point, in the figure, is shown as small sphere for visual emphasis only)

A distance in the coordinate system is measured with a standard rigid linear length like that of a “meter” or a “foot”. A distance of 5 meters, for example, is 5 times the length of the standard length of a meter. On the other hand, an angle is defined as a ratio of lengths and is dimensional-less. Hence, measurement of direction is indirectly equivalent to the measurement of distances only.

The coordinate system represents the system of rigid body like earth, which is embodied by an observer, making measurements. Since measurements are implemented by the observer, they (the measurements in the coordinate system) represent distance and direction as seen by the observer. It is, therefore, clearly implied that measurements in the coordinates system are specific to the state of motion of the coordinate system.

In a plane language, we can say that the description of motion is specific to a system of rigid bodies, which involves measurement of distance and direction. The measurements are done, using standards of length, by an observer, who is at rest with the system of rigid bodies. The observer makes use of a coordinate system attached to the system of rigid bodies and uses the same as reference to make measurements.

It is apparent that the terms “system of rigid bodies”, “observer” and “coordinate system” etc. are similar in meaning; all of which conveys a system of reference for carrying out measurements to describe motion. We sum up the discussion thus far as :

1. Measurements of distance, direction and location in a coordinate system are specific to the system of rigid bodies, which serve as reference for both magnitude and direction.
2. Like point, distance and other aspects of motion, the concept of space is specific to the reference represented by coordinate system. It is, therefore, suggested that use of word “space” independent of coordinate system should be avoided and if used it must be kept in mind that it represents volumetric extent of a specific coordinate system. The concept of space, if used without caution, leads to an inaccurate understanding of the laws of nature.
3. Once the meanings of terms are clear, “the system of reference” or “frame of reference” or “rigid body system” or “observer” or “coordinate system” may be used interchangeably to denote an unique system for determination of motional quantities and the representation of a motion.

#### Questions & Answers

List the application of projectile
Luther Reply
How can we take advantage of our knowledge about motion?
Kenneth Reply
pls explain what is dimension of 1in length and -1 in time ,what's is there difference between them
Mercy Reply
what are scalars
Abdhool Reply
show that 1w= 10^7ergs^-1
Lawrence Reply
what's lamin's theorems and it's mathematics representative
Yusuf Reply
if the wavelength is double,what is the frequency of the wave
Ekanem Reply
What are the system of units
Jonah Reply
A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained
Samson Reply
58asagravitasnal firce
Amar
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
Riya
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
Mustapha
How MKS system is the subset of SI system?
Clash Reply
which colour has the shortest wavelength in the white light spectrum
Mustapha Reply
how do we add
Jennifer Reply
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
Abhyanshu Reply
x=5.8-3.22 x=2.58
sajjad

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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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