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Unformatted text preview: the same but the angle changes. Comparatively, both the angle and the magnitude of the vector change when the origin is moved. See figure f for values. See calculation details for further reference. 10 (f) Additional Analysis 1. Use the data from this experiment to construct a set of mathematical rules that describes the properties of a vector when the coordinate system is translated and/or rotated. For example, if vector A has magnitude A and components Ax and Ay in one coordinate system, how can we mathematically determine its magnitude, angle, and components in a coordinate system rotated by angle and translated by vector r? Using the data from this experiment, we found that one can mathematically determine a vector
that has been rotated by any angle calculations. In order to calculate the displacement vector between origin 1 and origin 2, the position of each origin is to be used. For instance, Origin 1 was posited at (0,0) and origin 2 at (
3.5,
4.5). The displacement vector and its angle can be found by the following mathematical equations: 2 + (Y1 + Y2)2 = 5.7 cm
1(Y/X) =
52.12° To calculate the vector R1 + R2 and R3 R1, we added and/or subtracted the x
components and y
components of each and thereafter used the Pythagorean theorem to calculate each resulting magnitude, angle, and components. These calculations and findings are outlined in calculation details, as stated in data analysis question #5. 11 Conclusion Throughout the completion of the lab, we handled two separate experiments pertaining to vector components such as displacement, position, and vector addition. We utilized coordinate systems in handling the vectors, namely the Cartesian coordinate system. I n our first experiment, we used vector addition to calculate total displacement vectors from partial pathway vectors that we created ourselves. While our calculations made by vector addition of the pathway vectors gave us relatively similar values to those which we measured, there was of course human errors which led to somewhat differing results. Our percent error was calculated by using our measured values for the total displacement vectors as our actual yield and our calculated values (made by vector add ition) as our theoretical yield. For r11, our percent error was 0.86%. For r12, percent error was 5.61%. For r21, percent error was 5.03%. For r22, percent error was 7.05%. We believe that our measurements (actual yield) were accurate due to our low percentages of error for each of the four displacements. Any error that did occur could be attributed to the low precision tools used to complete the lab. For the second experiment, procedure required that we used a vector square to explore translation and rotation of the coordinate system and the results from such translation and rotation as it pertains to vector components. We used three coordinate systems to measure three vectors from a point of origin to three separate points. In the first coordinate s ystem, our point of origin was set at the intersection of the established x and y
axes. In our second coordinate system, we used the exact same origin, but altered the angle...
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This note was uploaded on 01/30/2014 for the course PHYS PHYS1210 taught by Professor Dr.norton during the Fall '13 term at Tulane.
 Fall '13
 Dr.Norton
 Physics

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