## Cartesian and Polar Coordinates

**Cartesian Coordinates (x,y)**: A vector,

**V**, in a 2-D Cartesian coordinate system can be written as:

**V**=(V

_{x},V

_{y})=V

_{x}

**i**V

_{y}

**j**

_{x}and V

_{y}are referred to as the

*vector components*and

**i**and

**j**are unit vectors - vectors of length one - in the x and y directions respectively.

The **magnitude** of **V** is:

- |

**V**|=√(V

_{x}

^{2}V

_{y}

^{2})

**Polar Coordinates (r,θ)**: Written in polar coordinates,

**V**=(V

_{r},V

_{θ})=V

_{r}

**r**

**r**is a unit vector in the r direction (at an angle of θ counter-clockwise from the x-axis).

**Relations between Cartesian and polar coordinates**:

- V

_{r}= √(V

_{x}

^{2}V

_{y}

^{2})

V_{θ}=tan^{-1}(V_{y}/V_{x})

V_{x} = |**V**|cos(θ)

V_{y} = |**V**|sin(θ)

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