Unformatted text preview: displacements . In e²ect, we have been talking about the motion o± individual points, or the abstraction o± such motion ±or larger bodies obtained by replacing each body with its center o± mass. However, a complete description o± the motion o± solid bodies also involves rotation . A rotation o± 3space about the zaxis is most easily described in cylindrical coordinates: a point P with cylindrical coordinates ( r,θ,z ), under a counterclockwise rotation (seen ±rom above the xyplane) by α radians does not change its r or z coordinates, but its θ coordinate increases by α . Expressing this in rectangular coordinates, we see that the rotation about the zaxis by α radians counterclockwise (when seen ±rom above) moves the point with rectangular coordinates ( x,y,z ), where x = r cos θ y = r sin θ to the point x ( α ) = r cos( θ + α ) y ( α ) = r sin( θ + α ) z ( α ) = z....
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 Fall '08
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 Calculus, Determinant, Vectors, Euclidean geometry, Coordinate system, Polar coordinate system, Coordinate systems, Cylindrical coordinate system

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