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Explain Cylindrical co-ordinate system. State the transformation relation between Cartesian and Cylindrical co-ordinates .
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• just like in Cartesian system we obtain a point by intersection of three mutually perpendicular plane surfaces in this system also a point is obtained by intersection of three surfaces mutually perpendicular to each other.
• but all three surfaces are not plane surfaces one is cylinder and other two are plane surfaces.
• x,y,z axis are taken as reference imagine a hollow vertical cylinder of radius 'r' placed such that axis of the cylinder coincides with z- axis.

If you any point on the cylindrical surface it is at a same distance from the axis. Therefore we defined the cylinder surface as r = constant surface.

• consider now a plane vertical surface of which one edge coincides with z-axis The angle of rotation φ is measured from xz- plane as shown when we take any point on this plane every time the angle of the point with xz plane is φ. Thus we define this plane as φ = constant plane.
• The intersection of these two surfaces is a vertical line. But we need a point. Hence we need one more surface so take z = constant plane.
• Thus the intersection of vertical line with z = constant plane is a point, this point is (r,φ,z) in cylindrical system.

Conversion from cylindrical to cartesian