Module 1—Motion

Describing Directions

 

sign convention: a system for designating directions along a straight line; one direction is positive and the other is negative

The magnitude of a vector is expressed as a value with a unit. For example, the magnitude of a displacement vector could be expressed in metres, as in 5.6 m. When it comes to communicating the direction of a vector, there are a number of options. If the motion occurs along a straight line, which has only two possible directions, it is convenient to describe one direction as positive and the other as being negative. This arrangement is called a sign convention. Using a sign convention, east could be called the positive direction and west could be called the negative direction.

 

This photograph shows two chuckwagons racing.

© Jack Dagley/Dreamstime

In most situations, motion happens in more than the two directions of the first example, so a sign convention is not adequate. The horses in the photograph are rounding a turn, switching from moving south to east and, in the process, momentarily going at each of the directions between south and east. When compass bearings (north, south, east, west, and all the directions in between) are used to describe this sort of motion, it is called the navigator method. At other times, it’s more convenient to use an x-axis and a y-axis or the Cartesian method.

 


navigator method: a system for measuring directions using compass bearings

 

Cartesian method: a system for measuring directions using the x-axis and y-axis


 

Read

 

You can find out more about these two systems for describing directions by reading pages 76 to 78 in your textbook. Note how the units are included in the descriptions.

 

The illustration on the left shows a compass rose.

This illustration shows the navigator method.

The illustration on the right shows an x-axis and a y-axis.

This illustration shows the Cartesian method.

 

 


 

Self-Check

 

SC 3. The illustration on the right shows a position vector pointing at 149° using the Cartesian method. Describe this same direction in two different ways using the navigator method.

 

Check your work.
Self-Check Answer

 

SC 3. This direction could also be described as 59° W of N or as 31° N of W.

 

Try This

 

You can learn more about the navigator method and the Cartesian method by using a computer simulation. This simulation is a great way to explore the use of angles to describe vector directions. Note that the simulation uses slightly different terminology and further subdivides the Cartesian method into three additional categories. You will not need to know all the categories for this course, but it is an opportunity for you to extend your understanding if you wish.

 

System Used in the Textbook

System Used in the Simulation

navigator method

navigator method

Cartesian method

polar (positive): measuring angles counterclockwise from the x-axis

polar (positive & negative): measuring angles counterclockwise or clockwise from the x-axis

x and y coordinates: describing directions in terms of x and y components

 

If you keep in mind that the last three methods used in the simulation are actually just variations of the Cartesian method, you should be able to keep it all straight. Also keep in mind that velocity values are normally always stated with units. An exception is made in this case since this simulation cannot accommodate units, so the units are not shown here. In this situation, assume that the magnitude is measured in m/s.

 

Open the Vector Specification simulation; then begin with Method 1.

 

Method 1: Cartesian Method (Polar Positive)

 

Figure 1

TR 1. On the control panel of the simulation, select the “Polar (positive)” mode and enter 150 for the magnitude and 240 for the angle. Press “Enter.” Verify that the display matches Figure 1.

 

In this mode, an angle is measured from a reference line (shown dotted and pointing east) in the positive, counterclockwise direction that is indicated by the arc. Angles can range from 0° to 360°.

 

Note: 360° is equivalent to 0°.