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Consider the position vector a shown in the diagram below. a makes an angle with the positive x axis, as shown. Notion that 0 (a) Find the x and y components of a. (Leave your answer in terms of a = Tal.) (b) Now consider what happens when the coordinate system is rotated by 90° counter- clockwise, so that the new x'-axis points along the direction of the old y-axis. Find the x' and y' components of a. (That is, find the components of a in the rotated coordinate system.) y' X X' a but

Consider the position vector a shown in the diagram below. a makes an angle with the positive x axis, as shown. Notion that 0 (a) Find the x and y components of a. (Leave your answer in terms of a = Tal.) (b) Now consider what happens when the coordinate system is rotated by 90° counter- clockwise, so that the new x'-axis points along the direction of the old y-axis. Find the x' and y' components of a. (That is, find the components of a in the rotated coordinate system.) y' X X' a but

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Consider the position vector a shown in the diagram below. a makes an angle with the positive x axis, as shown. 0 X Tal.) (a) Find the x and y components of a. (Leave your answer in terms of a = (b) Now consider what happens when the coordinate system is rotated by 90° counter- clockwise, so that the new x'-axis points along the direction of the old y-axis. Find the x' and y' components of a. (That is, find the components of a in the rotated coordinate system.) a y' TO Notice that we have rotated the coordinate system, but not the vector. In other words, the coordinates (x, y) of vector a in the original reference frame are different than the coordinates (x', y') in the rotated reference frame. But the vector has not changed (its length is the same and it still points in the same direction). This is because a vector exists in the absence of a coordinate system: Any vector is fully defined by a magnitude (a length) and a direction. The same vector has different representations in different reference systems.
Transcribed Image Text:Consider the position vector a shown in the diagram below. a makes an angle with the positive x axis, as shown. 0 X Tal.) (a) Find the x and y components of a. (Leave your answer in terms of a = (b) Now consider what happens when the coordinate system is rotated by 90° counter- clockwise, so that the new x'-axis points along the direction of the old y-axis. Find the x' and y' components of a. (That is, find the components of a in the rotated coordinate system.) a y' TO Notice that we have rotated the coordinate system, but not the vector. In other words, the coordinates (x, y) of vector a in the original reference frame are different than the coordinates (x', y') in the rotated reference frame. But the vector has not changed (its length is the same and it still points in the same direction). This is because a vector exists in the absence of a coordinate system: Any vector is fully defined by a magnitude (a length) and a direction. The same vector has different representations in different reference systems.
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