Lecture 5

Lecture 5 - Last Lecture Physics 231 General University...

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Physics 231 General University Physics Spring 2007 Lecture 5 Last Lecture ± Constant acceleration ± Kinematic equations Today ± Properties of Vectors ± Components ± Adding Vectors Algebraically Coordinate Systems ± Used to describe the position of a point in space ± Coordinate system consists of ± a fixed reference point called the origin ± specific axes with scales and labels ± instructions on how to label a point relative to the origin and the axes Cartesian Coordinate System ± Also called rectangular coordinate system ± x - and y - axes intersect at the origin ± Points are labeled ( x , y ) ± Scales (m, cm, mi, etc.) Rene Descartes (cm) (cm) Polar Coordinate System ± 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 , ) ± Scales
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Polar to Cartesian Coordinates ± Based on forming a right triangle from r and θ ± x = r cos θ ± y = r sin θ Cartesian to Polar Coordinates ± r is the hypotenuse and θ an angle ± θ must be counter-clock- wise (ccw) from positive x axis for these equations to be valid 22 tan y x rx y θ = =+ 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 (3 . 5 0 m ) (2 . 5 0 m ) 4 . 3 0 m rxy =+= + = 2.50 m tan 0.714 3.50 m 216 y x == = Note: not 36 D 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. 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 G 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
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This note was uploaded on 11/16/2010 for the course PHY 231 taught by Professor Ellis during the Spring '08 term at Kentucky.

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Lecture 5 - Last Lecture Physics 231 General University...

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