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## Rotation in Two Dimensions

Suppose we have a point A in a plane with perpendicular  x  and  y  coordinate axes scribed on it, as pictured in Fig. 23.4.

We can scribe a different pair of perpendicular coordinate axes  x'  and  y'  on the same plane surface using dashed lines by simply rotating the original coordinate axes by an angle    about their common origin, the coordinates of which are (0,0) in either coordinate system.

Now suppose that we have the coordinates  (xA,yA)  of point A in the original coordinate system and we would like to transform these coordinates into the coordinates   (x'A,y'A)  of the same point in the new coordinate system.23.14 How do we do it? By trigonometry, of course. You can figure this out for yourself. The transformation is

 x' = (23.2) y' = (23.3)

Next: Rotating Space into Time Up: A Rotational Analogy Previous: A Rotational Analogy
Jess H. Brewer - Last modified: Mon Nov 23 11:04:30 PST 2015