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Physics II workshop_Part_5

# Physics II workshop_Part_5 - Cartesian Representation A...

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12 Cartesian Representation A vector can be broken up into the sum of two vectors, one parallel to the x-axis, one parallel to the y- axis. The scalar lengths of the two vectors above are given from trigonometry, in equation 3-5 of text. These are called the components of the vector, and can be positive, negative, or zero. a x = r a cos θ and a y = r a sin ( Polar to Cartesian conversion) The Cartesian representation of a two dimensional vector is the two components, (a x , a y ) It is more common in physics and engineering to write the Cartesian form with unit vectors, r a = a x ˆ i + a y ˆ j The unit vectors have magnitude 1. Cartesian to Polar Conversion . If we know the components we get the polar form from r a =+ a x 2 + a y 2 and tan = a y a x . There is one remaining wrinkle: inverse tangent is a function that returns two distinct answers, the (angle) and the (angle + pi). Calculators return only one of these, it is up to you to determine the proper quadrant and pick the proper angle. e.g. r a =− 3.0 cm () ˆ i +− 6.0 cm ˆ j r a =

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Physics II workshop_Part_5 - Cartesian Representation A...

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