0.9 Phy1060: motion -- displacement and vectors  (Page 3/13)

Also in those cases, I will provide a table of key-value pairs that explain how the Braille keys in the image relate to text or objects in the image.

Displacement

As mentioned above, if one body is moved with respect to another body, either one of them may be said to have had a displacement .

Displacement is not the same as distance

Assume, for example, that you go to the local high school and run five laps around the track, stopping exactly where you started. The distance that you haverun will be the length of the path that you followed while running. However, while you may be completely out of breath by that point in time, the magnitudeof your displacement will have been zero.

Scalars versus vectors

Distance is a scalar quantity, while displacement is a vector quantity. Scalar quantities have only magnitude, such as three kilometers.

Vector quantities have two parts: magnitude and direction . For example, you might describe a vector quantity as having a magnitude of three kilometers and adirection of northwest.

Magnitude and direction

A displacement vector must have both magnitude and direction. For example, if you were to run about three-fourths of the way around the track, the distancethat you ran would be the length of your path.

However, the magnitude of your displacement would be the straight-line distance from your starting point to your stopping point.

The direction of your displacement would be an angle measured between some reference (such as due east, for example) and an imaginary line connecting yourstarting point and your stopping point.

If you stop where you start...

Getting back to the original proposition, if your stopping point is exactly the same as your starting point, the magnitude of your displacement vector willbe zero and the angle of your displacement vector will be indeterminate.

Vector notation

Assume that there are three spots marked on the top of a table as A, B, and C. If an object is moved from A to B and then from B to C, using vectors, it maybe stated that:

vecAC = vecAB + vecBC

where vecAB, vecBC, and vecAC represent vectors.

Typical notation

A typical notation for a vector in a physics textbook is something like AB, possibly in boldface and/or italics, with a small arrow drawn above the twoletters. However, there is no such small arrow on a QWERTY keyboard, and even if there were, it might not be compatible with your screen reader and/or yourBraille display.

My alternative notation

Therefore, I will use the following notation

vecAB

to indicate a vector extending from the spot labeled A to the spot labeled B.

In order to determine direction in an unambiguous way, you often need to know where the vector starts (the tail) and where it ends (the head). The notation used aboveindicates that the tail of the vector is at A and the head is at B.

In some cases, particularly in JavaScript code where a vector is defined by magnitude and direction instead of by a starting point and an ending point, Iwill refer to a vector simply as

vecA, vecB, etc.