# Uniform circular motion in a plane: differentiation of exponentials of imaginary vectors

July 6, 2009 Leave a comment

The position of a point in circular motion about the origin is given by

where is the radius of rotation, is the angular frequency, and is the rotational phase angle. The velocity and acceleration of the particle is obtained by differentiating its position with respect to time:

These may be rewritten as

Notice that the position vector of the particle is perpendicular to its velocity and opposite to its acceleration . In terms of rectangular coordinates, these quantities are

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