{"id":195,"date":"2020-04-19T15:58:31","date_gmt":"2020-04-19T19:58:31","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/chapter\/2-2-vectors-scalars-and-coordinate-systems\/"},"modified":"2020-06-03T23:24:56","modified_gmt":"2020-06-04T03:24:56","slug":"2-2-vectors-scalars-and-coordinate-systems","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/chapter\/2-2-vectors-scalars-and-coordinate-systems\/","title":{"raw":"3.2 Vectors, Scalars, and Coordinate Systems","rendered":"3.2 Vectors, Scalars, and Coordinate Systems"},"content":{"raw":"
<\/figure>\r\n[caption id=\"attachment_1710\" align=\"aligncenter\" width=\"362\"]\"\" Figure 1. The motion of this skateboarder can be described in terms of the distance he traveled (a scalar quantity) or his displacement in a specific direction (a vector quantity). In order to specify the direction of motion, its displacement must be described based on a coordinate system. \u00a0(credit: Julien Lanoy, Unsplash).[\/caption]\r\n
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What is the difference between distance and displacement? Whereas displacement is defined by both direction and magnitude, distance is defined only by magnitude. Displacement is an example of a vector quantity. Distance is an example of a scalar quantity. A vector<\/span> <\/strong>is any quantity with both magnitude and direction<\/em>. Other examples of vectors include a velocity of 90 km\/h east and a force of 500 newtons straight down.<\/p>\r\n

The direction of a vector in one-dimensional motion is given simply by a plus (+) or minus (\u2212) sign. Vectors are represented graphically by arrows. An arrow used to represent a vector has a length proportional to the vector\u2019s magnitude (e.g., the larger the magnitude, the longer the length of the vector) and points in the same direction as the vector. When writing a vector quantity, a horizontal arrow is used over the top of the variable. For example, [latex]\\overrightarrow{\\mathbf{p}}[\/latex] indicates that position is a vector variable, having both a magnitude and direction associated with it.<\/p>\r\n

Some physical quantities, like distance, either have no direction or none is specified. A scalar<\/span> <\/strong>is any quantity that has a magnitude, but no direction. For example, a 20 \u00b0C temperature, the 250 kilocalories (250 Calories) of energy in a candy bar, a 90 km\/h speed limit, a person\u2019s 1.8 m height, and a distance of 2.0 m are all scalars\u2014quantities with no specified direction. Note, however, that a scalar can be negative, such as a -20 \u00b0C temperature. In this case, the minus sign indicates a point on a scale rather than a direction. Scalars are never represented by arrows.<\/p>\r\n\r\n

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Coordinate Systems for One-Dimensional Motion<\/h1>\r\n

In order to describe the direction of a vector quantity, you must designate a coordinate system within the reference frame. For one-dimensional motion, this is a simple coordinate system consisting of a one-dimensional coordinate line. In general, when describing horizontal motion, motion to the right is usually considered positive, and motion to the left is considered negative. With vertical motion, motion up is usually positive and motion down is negative. In some cases, however, as with the jet shown above,\u00a0 it can be more convenient to switch the positive and negative directions. For example, if you are analyzing the motion of falling objects, it can be useful to define downwards as the positive direction. If people in a race are running to the left, it is useful to define left as the positive direction. It does not matter as long as the system is clear and consistent. Once you assign a positive direction and start solving a problem, you cannot change it.<\/p>\r\n\r\n<\/section>

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\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"244\"]\"An<\/a> Figure 2.<\/strong> It is usually convenient to consider motion upward or to the right as positive (+)<\/strong> and motion downward or to the left as negative (\u2212)<\/strong>.[\/caption]<\/figure>\r\nThis are called the Cartesian Coordinates in honour of Rene Descartes who first proposed them in the 17th Century.\r\n

Section Summary<\/h1>\r\n<\/section>
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