ch3+1410+FA11.key - Chapter 3 Vectors and Two-Dimensional...

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Vectors and Two-Dimensional Motion Chapter 3
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Cartesian Plane polar Types of Coordinate Systems 5
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Also called rectangular coordinate system x- and y- axes Points are labeled (x,y) Cartesian coordinate system 6
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Origin and reference line are noted Point is distance r from the origin in the direction of angle θ , ccw from reference line Points are labeled (r, θ ) Plane polar coordinate system 7
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Ex: Coordinate Systems A friend walks 3 meters due west, then turns and walks an additional 4 meters due north. What is the straight line distance between you and your friend (aka, “as the crow flies”) What direction (compass heading) would you need to be pointing to toss them their car keys? 8
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Solution 9
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Ex: Coordinate Systems and distance Lets say another friend walks due east for 5 meters, then turns north and walks an additional 3 meters. How far is this friend from the original friend (“as the crow flies)? What compass heading would this friend read if they were looking at the other friend? 10
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Vectors and Abstraction Vectors are simultaneously abstract and common This is the first step in mathematical abstraction that applies equally to two, three, four, ..., dimentions. Physicists and mathematicians regularly extend these basic ideas to describe phenomenal unexplainable by ordinary perception
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All physical quantities encountered in this text will be either a scalar or a vector A vector quantity has both magnitude (size) and direction A scalar is completely specified by only a magnitude (size) Why do you think it’s called a scalar? Vector vs. Scalar Review
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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 Properties of Vectors
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Negative Vectors Two vectors are negative if they have the same magnitude but are 180° apart (opposite directions) Resultant Vector The resultant vector is the sum of a given set of vectors More Properties of Vectors
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When adding vectors, their directions must be taken into account Units must be the same Geometric Methods Use scale drawings Algebraic Methods More convenient Adding Vectors
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Choose a scale Draw the first vector with the appropriate length and in the direction specified, with respect to a coordinate system Draw the next vector with the appropriate length and in the direction specified, with respect to a coordinate system whose origin is the end of vector and parallel to the coordinate system used for Adding Vectors Geometrically (Triangle or Polygon Method)
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Continue drawing the vectors “tip-to-tail” The resultant is drawn from the origin of to the end of the last vector Measure the length of and its angle Use the scale factor to convert length to actual magnitude Graphically Adding Vectors, cont.
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When you have many vectors,
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