Vector Direction - Questions 18 Help

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Vector quantities are quantities like displacement and force (to name just two) that are fully described by expressing a magnitude (or numerical value) and a direction. Agreed-upon conventions are required to express the direction of any vector that is not aligned with the traditional east-west-north-south compass directions. The counter-clockwise from east convention expresses the direction of a vector as the counter-clockwise angle of rotation that the vector makes with due east. A second convention involves identifying the angle and direction of rotation that the vector makes with one of the two nearby axes (or compass directions).

There are three similar versions of this question. Each includes a fourth quadrant vector whose direction is given as an angle of rotation South of East. The task involves determining the direction of the vector as expressed using the Counter-Clockwise from East convention. One of the versions is shown below.

Version 1:

Perform the following convention conversion for the given direction.
Convert 67° S of E to the counter-clockwise from east convention.

This question involves a conversion of direction information from one convention to another convention. A diagram is not given. However, it is strongly recommended that a diagram be drawn on some scratch paper in order to facilitate the thinking through of the conversion.

All versions of questions in this question group involve a South and East vector; the vector is described as being a certain angle "South of East." To describe a vector as being "20° South of East" means that the vector is 20° from East in the southern direction. That is, the vector is South of East by 20° and not North of East. On the other hand "20° East of South" means that the vector is 20° from the the South compass direction, rotated towards the East. Use this information to help you sketch your vector on scratch paper.

Picture a vector pointing East and then being rotated about its tail. By the time it is rotated 90° counter-clockwise, it would be pointing North. Thus North is 90°. If the same vector were rotated 180° from the East starting direction, then it would be pointing West. So West is 180°. And if this East vector is rotated 270° in the counter-clockwise direction, it will be pointing South. So South is 270°. If the vector is rotated in a complete 360° circle then it will be pointing east once more. So East is both 0° and 360°. The vector in this question has a CCW direction between 270° and 360°. You can think of it being short of 360° by a certain angle and more than 270° by another angle. Once you sketch the vector, determine the angle it makes with East and/or with South. Adding the angle it makes with South to 270° will give you the CCW direction. Similarly, subtracting the angle it makes with East from 360° will give you the same CCW direction.

Try this link to The Physics Classroom Tutorial for more help with vector direction:

Vector Direction