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Chapter 3 Notes - Chapter 3 Notes Coordinate...

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Chapter 3 Notes - Coordinate Systems—Cartesian (for 2 dimensions and 3 dimensions) o Origin - fixed point of reference o Axes - scales and labels o Instructions - how to label a point relative to origin and axes o It’s basically a grid x is positive to the left, y is positive up Find ourselves by finding a pair of 2 numbers ( x , y ) o For 3 dimensions you add the z coordinate (thus having 3 numbers) - Polar Coordinate System o = x r cosθ o = y r sinθ o = tanθ yx o = + r x2 y2 - Vectors and Scalars (used for multiple dimensions) o A scalar quantity is completely specified by a single value with the appropriate units and has not direction o Vector Quantity It is completely described by a number and appropriate units plus a direction o Vector example A particle travels from A to B along the path shown by the dotted 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 o Vector Representation Bold letter = A Letters with arrow = A Magnitude = A Magnitude shown as the non-bold letter for vector o A instead of A o Vector Addition Draw vectors “tail to tip” The resultant ( R ) is drawn from the tail of A to the tip of the last vector ( B ) R
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θ B Law of Cosines useful for getting magnitude when angles known = + - R2 A2 B2 2ABcosθ The two sums are the same vector = + + A B C + D = B + + + C D A Example 12. A car travels 20.0 km due north and then 35.0 km in a direction 60.0º west of north. Find the magnitude and direction of the car’s resultant displacement Vector Addition/Subtraction Rules The sum of 2 vectors is independent of the order of the addition o Commutative Law of Addition + = + A B B A The sum of 3 or more vectors is independent of how they are grouped o Associative Law of Addition + + = + + A B C A B C All of the vectors must have the same units All of the vectors must be of the same type of quantity you cannot add a displacement to a velocity!
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