General physics I, lec 2 By: T.A.Eleyan 1 Lecture 2 Coordinate Systems & Vectors

General physics I, lec 2 By: T.A.Eleyan 2 Coordinate Systems and Frames of Reference The location of a point on a line can be described by one coordinate; a point on a plane can be described by two coordinates; a point in a three dimensional volume can be described by three coordinates. In general, the number of coordinates equals the number of dimensions. A coordinate system consists of: 1. a fixed reference point (origin) 2. a set of axes with specified directions and scales 3. instructions that specify how to label a point in space relative to the origin and axes

General physics I, lec 2 By: T.A.Eleyan 3 Coordinate Systems In 1 dimension, only 1 kind of system,  Linear Coordinates (x) +/- In 2 dimensions there are two commonly used systems,  Cartesian Coordinates(x,y)  Polar Coordinates(r,  ) In 3 dimensions there are three commonly used systems,  Cartesian Coordinates(x,y,z)  Cylindrical Coordinates (r, ,z)  Spherical Coordinates(r,  )

General physics I, lec 2 By: T.A.Eleyan 4 Cartesian coordinate system also called rectangular coordinate system x and y axes points are labeled (x,y) Plane polar coordinate system  origin and reference line are noted  point is distance r from the origin in the direction of angle   points are labeled (r,  )

General physics I, lec 2 By: T.A.Eleyan 5 The relation between coordinates Furthermore, it follows that Problem: A point is located in polar coordinate system by the coordinate and. Find the x and y coordinates of this point, assuming the two coordinate systems have the same origin.

General physics I, lec 2 By: T.A.Eleyan 6 Example : The Cartesian coordinates of a point are given by (x,y)= (-3.5,-2.5) meter. Find the polar coordinate of this point. Solution: Note that you must use the signs of x and y to find that is in the third quadrant of coordinate system. That is not 36

General physics I, lec 2 By: T.A.Eleyan 7 Scalars and Vectors Scalars have magnitude only. Length, time, mass, speed and volume are examples of scalars. Vectors have magnitude and direction. The magnitude of is written Position, displacement, velocity, acceleration and force are examples of vector quantities.

General physics I, lec 2 By: T.A.Eleyan 8 Properties of Vectors Equality of Two Vectors Two vectors are equal if they have the same magnitude and the same direction Movement of vectors in a diagram Any vector can be moved parallel to itself without being affected

General physics I, lec 2 By: T.A.Eleyan 9 Negative Vectors Two vectors are negative if they have the same magnitude but are 180° apart (opposite directions) Multiplication or division of a vector by a scalar results in a vector for which (a) only the magnitude changes if the scalar is positive (b) the magnitude changes and the direction is reversed if the scalar is negative.

General physics I, lec 2 By: T.A.Eleyan 10 Adding Vectors When adding vectors, their directions must be taken into account and units must be the same First: Graphical Methods Second: Algebraic Methods

General physics I, lec 2 By: T.A.Eleyan 11 Adding Vectors Graphically (Triangle Method) Continue drawing the vectors “tip-to-tail” The resultant is drawn from the origin of A to the end of the last vector Measure the length of R and its angle

General physics I, lec 2 By: T.A.Eleyan 12 When you have many vectors, just keep repeating the process until all are included The resultant is still drawn from the origin of the first vector to the end of the last vector

General physics I, lec 2 By: T.A.Eleyan 13 Alternative Graphical Method (Parallelogram Method) When you have only two vectors, you may use the Parallelogram Method All vectors, including the resultant, are drawn from a common origin The remaining sides of the parallelogram are sketched to determine the diagonal, R

General physics I, lec 2 By: T.A.Eleyan 14 Vector Subtraction Special case of vector addition If A – B, then use A+(-B) Continue with standard vector addition procedure