chapter3

chapter3 - Chapter 3 Vectors Vectors Vector quantities...

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Chapter 3 Vectors
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Vectors Vector quantities ± Physical quantities that have both numerical and directional properties Mathematical operations of vectors in this chapter ± Addition ± Subtraction Introduction
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Coordinate Systems Used to describe the position of a point in space Common coordinate systems are: ± Cartesian ± Polar Section 3.1
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Cartesian Coordinate System Also called rectangular coordinate system x - and y - axes intersect at the origin Points are labeled ( x , y ) Section 3.1
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Polar Coordinate System Origin and reference line are noted Point is distance r from the origin in the direction of angle T , ccw from reference line ± The reference line is often the x- axis. Points are labeled ( r , ) Section 3.1
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Polar to Cartesian Coordinates Based on forming a right triangle from r and T x = r cos y = r sin If the Cartesian coordinates are known: 22 tan y x rx y ± Section 3.1
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Example 3.1 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. Solution: From Equation 3.4, and from Equation 3.3, ± ² ± ² 22 ( 3.50 m) ( 2.50 m) 4.30 m rx y 2.50 m tan 0.714 3.50 m 216 (signs give quadrant) y x T ² ² q Section 3.1
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Vectors and Scalars A scalar quantity is completely specified by a single value with an appropriate unit and has no direction. ± Many are always positive ± Some may be positive or negative ± Rules for ordinary arithmetic are used to manipulate scalar quantities. A vector quantity is completely described by a number and appropriate units plus a direction. Section 3.2
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Vector Example A particle travels from A to B along the path shown by the broken line. ± This is the distance traveled and is a scalar. The displacement is the solid line from A to B ± The displacement is independent of the path taken between the two points. ± Displacement is a vector. Section 3.2
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Vector Notation Text uses bold with arrow to denote a vector: Also used for printing is simple bold print: A When dealing with just the magnitude of a vector in print, an italic letter will be used: A or | | ± The magnitude of the vector has physical units. ± The magnitude of a vector is always a positive number. When handwritten, use an arrow: A & A & A & Section 3.2
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Equality of Two Vectors Two vectors are equal if they have the same magnitude and the same direction. if A = B and they point along parallel lines All of the vectors shown are equal. Allows a vector to be moved to a position parallel to itself AB && Section 3.3
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Adding Vectors Vector addition is very different from adding scalar quantities. When adding vectors, their directions must be taken into account.
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This note was uploaded on 02/12/2011 for the course PHYS 111 taught by Professor Moro during the Spring '08 term at NJIT.

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chapter3 - Chapter 3 Vectors Vectors Vector quantities...

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