L02d - 1 11 Physics 111 Lecture 2d “Mathematics is the...

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Unformatted text preview: 1 / 11 Physics 111 Lecture 2d “Mathematics is the door and the key to the sciences.” –Roger Bacon Coordinate system Coordinate system Vectors Subtraction Question Components Components 2 / 11 ■ A coordinate system consists of a fixed reference point (the origin) and fixed reference lines (the axes) ■ Coordinate systems are used to specify points in space ■ In 1D, it is just a line (see figure) ■ In 2D, it is two perpendicular lines (see figure) ■ In 2D, we can specify the position of a point by means of its rectangular coordinates ( x,y ) or by means of polar coordinates ( R,θ ) (see figure) Coordinate system Coordinate system Vectors Subtraction Question Components Components 3 / 11 ■ Rectangular and polar coordinates are related by x = R cos( θ ) (1) y = R sin( θ ) (2) R = radicalbig x 2 + y 2 (3) θ = tan- 1 parenleftBig y x parenrightBig (4) ■ Example. Find the polar components of the point (- 2 . 3 , 5 . 4) ■ Bad news: θ is somewhat ambiguous ■ Sign of angle: CCW is positive, CW is negative Vectors Coordinate system Vectors Subtraction Question Components Components 4 / 11 ■ Scalars are quantities that only have magnitude...
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L02d - 1 11 Physics 111 Lecture 2d “Mathematics is the...

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