CH3 - Chapter 3 Vectors Vectors and Scalars A scalar...

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Chapter 3 Vectors
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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. A vector quantity is completely described by a number and appropriate units plus a direction. Can you answer first question on Objective test sheet?
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Vectors We make life Easy!
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Vector Notation When handwritten, use an arrow: When printed, will be in bold print: A When dealing with just the magnitude of a vector in print, an italic letter will be used: A or | A | The magnitude of the vector has physical units The magnitude of a vector is always a positive number A
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Vector Example A particle travels from A to B along the path shown by the dotted red 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
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Equality of Two Vectors Two vectors are equal if they have the same magnitude and the same direction A = B if A = B and they point along parallel lines All of the vectors shown are equal
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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 )
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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 , counter clockwise from reference line Points are labeled ( r , )
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Polar to Cartesian Coordinates Based on forming a right triangle from r and x = r cos y = r sin
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Cartesian to Polar Coordinates r is the hypotenuse and an angle must be ccw from positive x axis for these equations to be valid 2 2 tan y x r x y
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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: and, 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
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Adding Vectors When adding vectors, their directions must be taken into account Units must be the same Graphical Methods Use scale drawings Algebraic Methods More convenient
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Adding Vectors Graphically 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 A and parallel to the coordinate system used for A
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Adding Vectors Graphically, cont. Continue drawing the
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This note was uploaded on 10/21/2010 for the course PHY 2048 taught by Professor Bose during the Spring '08 term at University of Central Florida.

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CH3 - Chapter 3 Vectors Vectors and Scalars A scalar...

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