PHY183-Lecture30 - Announcement Clicker points(thru Mar 2...

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March 19, 2006 1 Engineers 1 Engineers 1 Spring Semester 2006 Lecture 30 March 19, 2006 2 Announcement Announcement ! Clicker points (thru Mar 2) posted on Lon-Capa Maximum points: 88 Scores out of 1/2 maximum = 44 ! Currently 4 students without registered clicker codes: adamsb14, hillyerb, labeffda, spearsj3 ! Currently scores for 3 unregistered clickers: 162335, 263787, 1291195 ! If this is you, please contact us. March 19, 2006 3 Circular Motion Circular Motion ! Motion along the perimeter of a circle March 19, 2006 4 Polar Coordinates Polar Coordinates ! We want to know the equations that govern the position vector as a function of time, ! x and y coordinates change along trajectory, but distance to origin stays the same ! 2-dimensional motion can be reduced to 1d motion ! Introduce polar coordinates r = length of vector = angle of vector relative to the x -axis r r ( t ) = ( x ( t ), y ( t )) = x ( t ) ˆ x + y ( t ) ˆ y r r r r !
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March 19, 2006 5 Polar and Cartesian Coordinates Polar and Cartesian Coordinates ! Transformation from Cartesian to polar coordinates ! Transformation from polar to Cartesian coordinates r = x 2 + y 2 ! = arctan y x " # $ % x = r cos y = r sin March 19, 2006 6 Unit Vectors in Polar Coordinates Unit Vectors in Polar Coordinates ! Two-dimensional space: need two unit vectors ! Cartesian: x and y directions ! Polar: radial ( r ) and tangential ( t ) ! Unit vectors are orthonormal
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This note was uploaded on 03/19/2008 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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PHY183-Lecture30 - Announcement Clicker points(thru Mar 2...

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