In complete analogy to one-dimensional linear motion, in which the displacement vector was written as x, we can define the angular displacement vector $\theta$.

The angular distance,

is the scalar corresponding to linear distance.

The two most commonly used angular measures are:

• Degrees (^o): 360^o in one complete circle
• Radians (rad): 2$\pi$ radians in one complete circle

A radian is a dimensionless quantity, a pure number.

The relationship between arc length and radius can be seen from the figure on the right:

If s = r, then $\theta$ = 1 rad, and by definition, 1 rad = 57.29578^o

Here is a utility that does all of these conversions for you in Java Script.

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