Physics Tutorial: Position and Reference Point

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In this Physics tutorial, you will learn:

The meaning of Reference Point
What is Position?
What is Location and where does it differ from Position?
How to express the Position in a system of coordinates?

Introduction

In the previous Physics Tutorial, "Types of Motion", we described the motion as "the phenomenon in which an object changes its location over time." But, is it always easy to know whether an object is moving or not?

Consider the following examples:

You are looking at the downloading bar on a PC screen when a very heavy file is being downloaded and the internet is very slow.
You are observing the stars during the night in a clear sky.
You are looking the minutes hand of a wall clock.

Is it easy to detect any motion in the above examples? Why?

Which action would help you find whether the abovementioned objects are moving or not? Why?

The meaning of reference point

Let's try to explain the concept of reference point by providing answers to the questions posed in the "Introduction" section.

1. The downloading bar seems unmoveable. At first sight, it seems the downloading process has stopped. You can check this by putting the cursor at the end of the orange bar, which shows the downloading progress. After a while, you can check whether the orange bar has moved on the right of the cursor or not. If yes, the downloading process is active. Therefore, the cursor acts as a reference point for you as it helps understanding whether the downloading progress bar is moving or not.

Look at the figure below:

Physics Tutorials: This image shows a downloading image with two seperate download bar rates to indictae the tracking of motion through time

2. The bright star is slightly on the left of pyramid in the first figure. After a while, it "shifts" on the right of the pyramid. In this way, the pyramid acts as a reference point, which helps us to understand whether the stars are in the same place as before or they "have moved".

Look at the figure:

Physics Tutorials: This image shows two similar pictures of the stars, one above the other. Each image of the stars has a white triangle and a single bright star. On the first image, the star is above the trianlge, on the second image, the star is to the right of the triangle. This image helps to illustrate how we can visualise movement from looking at the stars using a pryamid (or triangle as shown in the images) to track relative motivon

3. In the figure below, the star in the wall helps us understand that the clock is working properly as the minute hand has moved in respect to the star. Therefore, it (the star) acts as a reference point.

Physics Tutorials: This image shows two basic clock faces, the first indicating 10:10 am, the second 10:15am to illustrate the passing of time and motion of the clock to measure time in equal units

In all the above examples, it was clearly outlined the necessity and importance of a reference point from which we start making any measurement or estimation in order to detect any change in object's location.

Thus, by definition, "A fixed point with respect to which a body changes its location is called Reference Point or Origin."

When dealing with calculations in Kinematics, reference point is usually the origin of the coordinate system, no matter whether the system is 1, 2 or 3 dimensional. Reference point (origin) is usually denoted by the number 0 or the letter O.

What is Position? How does it differ from Location?

We can show the location of an object by a finger, or by drawing a small dot in the place where the object lies. If the object is voluminous, we usually put a small dot at the object's centre to show its location as in the figure below.

Physics Tutorials: This image shows a hexagon with a dot in the exact middle to illustrate position within an object.

It is obvious that location does not imply the use of any reference point or coordinate. Therefore, no numerical values are involved when dealing with the location of an object.

On the other hand, Position is a physical quantity that shows how far an object from the origin (reference point) is. Position not only has a magnitude (numerical value) but it also has a direction. It is not the same thing if we say, "the object is 6m on the left of the reference point" and "the object is 6m on the right of the reference point" although the distance from the origin (reference point) is the same in both cases (6 m).

Physics Tutorials: This image shows a tree in the centre with two people, one either side of the tree at 6 meters distance from the tree, twelve meters distant from each other

Thus, there are two men in the figure; each of them is at 6m from the tree, which in this case acts as a reference point or origin. Therefore, it is obvious it is not enough knowing only the distance from the reference point but we must know the direction as well. Only then, we can exactly determine the position of a given object.

As we discussed in Physics Tutorial 2.1 "Vectors and Scalars in Physics", a quantity for which direction information is required is known as "vector quantity." This is the case for the position of an object.

By definition, "Position is a vector quantity that shows how far an object is from the origin in a given direction."

Position can be positive, negative or zero. It can be positive when the location of the object is at the positive part of the position axis. For example, the position of the green bicycle shown below is positive as its location is at (+4) m. As for the position of the blue bicycle, it is negative because its location is at (-1) m. (Remember, for voluminous and irregularly shaped objects we consider the actual location at the centre of the object). Position can be zero when the object is located at the reference point.

Physics Tutorials: This image shows a horizontal scale which is numbered from minus two through to 5. There are two bicycles placed on the scale, the first, coloured blue, is as the minus two position, the second, coloured green, is at the plus three position.

Position in the system of coordinates

It is known that in a system of coordinates we can assign a letter to each direction available. Thus, if there is only one direction available (1-D) as shown in the above figure, we denote the axis by the letter x and the object's position by the vector x⃗ or Ox)⃗. We can write

x⃗_{blue bicycle} = -1 m

and

x⃗_{green bicycle} = +4 m

When two directions of motion (2-D) are available, we can express the position of an object using a pair or coordinates (one for each direction). We must use two letters (usually x and y) to label the directions. Therefore, we need to know both coordinates to determine the location of an object in 2-D. Look at the figure below:

Physics Tutorials: This image shows a grid with point A marked as grid position 2y,4x

From the above graph, we can see that the object A is 4m on the right and 2m above the reference point. Therefore, we say the position of the object A is at (4m, 2m) and by this, we understand that the position of object A is represented through the vector

OA⃗ = 4m/2m

and the object A is

|OA⃗| = √OA²_x + OA²_y
= √4m² + 2m²
= √20m²
= 4.47m

away from the origin in the direction of the vector OA⃗.

Likewise, we can use the same approaches in 3-D (in space) as well. We have another direction added in this case. Usually, it is denoted by the letter z. Therefore, we must write all three coordinates to determine the position of an object. Look at the graph below.

Physics Tutorials: This image shows the grid position 5y,6x and 5z to indicate the three dimensional grid coordinates for position reference on a three dimensional plain

The object A is in the 3 dimensional space. It is diverted 6m from the origin according the x-direction, 5 m from the origin in the y-direction and 6m from the origin in the z-direction, all in the positive direction. This means the components of the vector OA⃗ which represents geometrically the linear distance from the origin, are OAx = 6m, OAy = 5m and OAz = 6m respectively.

From the concept of vector's magnitude, we know that

|OA⃗| = √OA²_x + OA²_y + OA²_z

Therefore, substituting the values, we obtain for the magnitude of the vector OA⃗

|OA⃗| = √(6m)² + (5m)² + (6m)²
= √36m² + 25m² + 36m²
= √97m²
= 9.85m
≈ 10m

Thus, the object A is nearly 10m away from the origin (reference point) in the direction of the vector OA⃗.

Example 1

Write the position of the objects A, B and C shown in the figure. How far are they from the origin?

Physics Tutorials: This image expands on the prvious chart to short tthree refence points (A, B and C) to visually illustrate the coordinates on a three dimensional plain

Solution 1

The object A is in the xOy plane. It has no z-coordinate, so we need to know only two coordinates to show its position.

From the figure, we can see that Ax = 4m, Ay = 3m (and Az = 0m). Therefore, the position OA⃗ of the object A is

OA⃗ = 4m3m0

The distance from the origin of the Object A is found by calculating the magnitude of the vector OA⃗. Therefore, using the known procedure explained in the article "Vectors and Scalars" for calculating the magnitude of a vector, we can write

|OA⃗| = √OA²_x + OA²_y + OA²_z

Substituting the values, we obtain for the magnitude of the vector OA⃗

|OA⃗| = √(4m)² + (3m)² + (0m)²
= √16m² + 9m²
= √25m²
= 5m

This means the point A is 5m away from the origin in the direction of the vector OA⃗.

The same procedure is used for the other two objects. Thus, for the object B we have only one coordinate Bz = 5m as it lies on the z-axis only. It is not necessary to calculate the magnitude of the vector OB⃗ as it is clear that |OB⃗|= 5m.

As for the object C, we can see from the figure that it contains all three coordinates. Thus, Cx = 3m, Cy = 6m and Cz = 4m. Therefore, the magnitude of the vector OC⃗ which represents the position of the object C (its linear distance from the origin), is

|OC⃗| = √OC²_x + OC²_y + OC²_z

Substituting the values, we obtain for the magnitude of the vector (OC)⃗

|OC⃗| = √(3m)² + (6m)² + (4m)²
= √9m² + 36m² + 16m²
= √61m²
= 7.81m

Therefore, the object C is 7.81m away from the origin in the direction of the vector OC⃗.

The figure below shows the position vectors for the three objects.

Physics Tutorials: This image shows the same chart as in the previous example with the addition of verctor arrows from the datam point in the direction of the final reference point

Remark! The 1 and 2 dimensional motions are special cases of the 3 dimensional motion. We can either write 0 in the place of the missing coordinates or simply represent the position in as many coordinates as given. We can illustrate this aspect using the position of the vector B. This position can be mathematically represented in three ways:

In one dimension (according z only)

OB⃗ = 5m

In two dimensions (according x and z, or y and z)

OB⃗ = 05m

In three dimensions (according x, y and z)

OB⃗ = 005m

All these three presentations show the same thing: the vector OB⃗. Hence, they are all equivalent.

Summary

A fixed point with respect to which a body changes its location is called Reference Point or Origin.

When dealing with calculations in Kinematics, the reference point is usually the origin of the coordinate system, no matter whether the system is 1, 2 or 3 dimensional. The reference point (origin) is usually denoted by the number 0 or the letter O.

The concept of Location is different from that of Position. Thus, Location does not imply the use of any reference point or coordinate. Therefore, no numerical values are involved when dealing with the location of an object.

On the other hand, Position is a physical quantity that shows how far an object from the origin (reference point) is. Position not only has a magnitude (numerical value) but it also has a direction. Given this, position can be positive, negative or zero depending on which part of the reference point it is.

In a system of coordinates, we can assign a letter to each direction available. Thus, if there is only one direction available (1-D), we denote the axis by the letter x and the object's position by the vector x⃗ or Ox⃗.

The 1 and 2 dimensional motions are special cases of the 3 dimensional motion. We can either write 0 in the place of the missing coordinates or simply represent the position in as many coordinates as given.

Position amd Reference Point Revision Questions

1. An airplane is 47 miles due North and 72 miles due West of the Command Centre of Air-Traffic Control at 6 miles of altitude. How far is the airplane from the Command Centre building? Express the answer to one decimal place (to one tenths of a mile).

86.0 miles
85.9 miles
125.0 miles
86.2 miles

Correct Answer: D

2. Which of the objects shown in the figure is closer to the origin?

Physics Tutorials: This image shows 4 reference point in a chart to support question tw o in the physics revision questions for position and reference.

Object A
Object B
Object C
Object D

Correct Answer: C

3. Which of the following statements is WRONG?

An object with coordinates (3m, 4m, 0m) has the same position as another object with coordinates (5m, 0m, 0m)
An object with coordinates (3m, 4m, 0m) has the same distance from the origin as another object with coordinates (5m, 0m, 0m)
An object with coordinates (3m, 4m, 0m) has the same location as another object with coordinates (5m, 0m, 0m)
An object with coordinates (3m, 4m, 0m) occupies the same space as another object with coordinates (5m, 0m, 0m)

Correct Answer: B

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