# Vectors - Chapter 3 - Vectors Coordinate Systems Used to...

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1 Chapter 3 - Vectors c Used to describe the position of a point in space c Coordinate system consists of b a fixed reference point called the origin b specific axes with scales and labels b instructions on how to label a point relative to the origin and the axes Coordinate Systems c Also called rectangular coordinate system c x - and y - axes intersect at the origin c Points are labeled ( x , y ) Polar Coordinate System b Point is distance r from the origin in the direction of angle θ , ccw from reference line b Points are labeled ( r , ) x = r cos , y = r sin 2 2 tan y x r x y = = + must be ccw from positive x axis for these equations to be valid Cartesian Coordinate system

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2 Example 3.1 c The Cartesian coordinates of a point in the xy plane are ( x,y ) = (-3.50, -2.50) m, as shown in the figure. Find the polar coordinates of this point. 2 2 2 2 ( 3.50 m) ( 2.50 m) 4.30 m r x y = + = + − = 2.50 m tan 0.714 3.50 m 216 y x θ = = = = ° c Solution: Vectors and Scalars c A scalar quantity is completely specified by a single value with an appropriate unit and has no direction. c A vector quantity is completely described by a number and appropriate units plus a direction. c When handwritten, use an arrow: c When printed, will be in bold print: A c When dealing with just the magnitude of a vector in print, an italic letter will be used: A or | A | c The magnitude of the vector has physical units c The magnitude of a vector is always a positive number Vector Notation A a
3 Vector Example c A particle travels from A to B along the path shown by the dotted red line b This is the distance traveled and is a scalar c The

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## This note was uploaded on 07/30/2011 for the course PHY 2048 taught by Professor Bose during the Spring '08 term at University of Central Florida.

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Vectors - Chapter 3 - Vectors Coordinate Systems Used to...

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