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Mathematics-Online course: Vector Calculus - Coordinates

# Rotating Frame of Reference

The left side of the picture given below shows the paths of a rectilineal and a circular motion:

On the right the two paths are pictured in a frame of reference rotating at an angular velocity . Hence, they are pictured as they would appear to an observer having a ride on a roundabout.

For the rectilineal motion the transformation of the coordinates yields

with

Since the factor within the brackets increases if the parameter does, we obtain a spiral. The pictured windings correspond to the time interval .

The path's shape of the circular motion in the frame rotating at cannot directly be seen from the transformed coordinates

As our example shows, the direction of the observed motion can change abruptly. Even bends can appear on the observed path. In such a singular point the observed velocity equals zeros with respect to the rotating frame.