Physics Phenomena

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Study Of Motion
Displaying motion with
Vectors






1. Quantities of Measurement are divided into two major categories. These categories are the scalar quantity (measurement) and the vector quantity (measurement).

Scalar Quantities (which contain no statement of direction) are the typical kinds of measurements most of us use in every day situations. Consider the following statement about the motion of an automobile.

"The automobile was traveling at 40 miles per hour (40 mi/h)." Notice that the measurement has a number and units, but no statement of direction. Scalar quantities always have a number and one or more units attached to the number, but never have any statement of direction attached to the quantity being expressed.

Vector Quantities (which do contain statements of direction) are not so typical kinds of measurements used by most of us in everyday situations. In fact vector quantities are seldom used outside of math, science, and engineering, except in descriptive conversations where someone is giving or describing directions. Consider the following statement about the motion af an automobile.

"The automobile was traveling at 40 miles per hour east (40 mi/h, E)." Notice that this measurement has a number and units as any scalar quantity would, but also contains a statement of direction. This statement of direction is what makes a seemingly ordinary scalar quantity into a vector quantity.

Consider the following Chart comparing scalar and vector quantities. (Note: N is for north, E is for east, W is for west, and S is for south)
 
 

Scalar vs Vector quantities (measurements)
Scalar Quantities Vector Quantities
Examples:

Distance; 100 km

Speed; 60 km / h; 10 m / s

Examples:

Displacement; 100 km, N

Velocity; 60 km / h, E; 10 m / s, W


 

The differences between scalar and vector quantities may seem to be unimportant to non science, non engineering individuals, but in science and engineering, these measurements are extremely important, because it affects things like safety in the design of machines that we constantly use everyday. Vectors are used to describe motion and forces correctly. Vectors are used to describe the motion and forces involved in a whole host of technologies that we use and often take for granted. The study and use of vectors ranges from baseballs to missiles, from bicycles to airplanes, from electrical appliances to particle accelerators, and so on.
 

2. How are vector quantities (measurements) represented?

The answer is by arrows. Any vector quantity can be and often is represented by an arrow. An arrow can represent the magnitude (size) of the vector quantity by its length and can represent the direction associated with it by the direction it points to.

Observe:
 
 

A few Examples of Displacement Vectors

----------> 10 m, E

---------------> 15 m, E

<---------- 10 m, W

<--------------- 15 m, W
 

Vectors can point in any direction defined by the compass. A compass, as you most likely know, is a device which contains a magnetized needle which points along the magnetic field lines between the earth's north and south magnetic poles. Though the magnetic poles are not exactly at the positions of the actual north and south poles as defined by the earth's rotational axis, they are close enough to these points to allow a compass to be used for simple navigation when an individual is in the temperate or equatorial zones of our planet. The closer one is to the north poles the greater the difference between the physical poles and the magnetic poles becomes. Good navigators know how to correct for this difference, though today many people, including navigators rely upon the Global Positioning System (GPS) which displays a persons position, based upon orbiting satellite identifying the position from the signal being broadcast by the device. Whether you are using an ordinary compass or a GPS device, the directions of motion are always defined by the N, S, E, W compass points. A compass measures 360 degrees (a complete circle) from N, defined as zero degrees, all the way around back to N, which can also be called 360 degrees.

Observe, and also NOTE that the designated directions NW, SE, SW, and NW are specifically at the mid-point between the N, E, S, and W directions. This means that they are at 45 degrees to any of the "Cardinal points" (N, E, S, and W). Any direction between any 2 of the "Cardinal points", not at 45 degrees to them, may NOT be designated as NE, SE, SW, and NW respectively.
 
 
 

Compass Points with degrees shown

 

How are vectors, such as displacement vectors represented using the compass directions?

The example which follows illustrates how this works.
 
 

Example of drawing a vector

3. Before you go on to Vector Resolution and Vector Addition, it is a good idea to review Right Angle Triangles. Use the link below to go to that topic.

Right Angle Triangles



4. Resolving Vectors into Components and Vector Addition: The Link below will take you to this topic.

Vector Resolution and Vector Addition

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