Angle of rotation
# Angle of rotation

In mathematics, the angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle. A clockwise rotation is considered a negative rotation, so that, for instance, a rotation of 310° (counterclockwise) can also be called a rotation of –50° (since 310° + 50° = 360°, a full turn). A counterclockwise rotation of more than one complete turn is normally measured modulo 360°, meaning that 360° is subtracted off as many times as possible to leave a non-negative measurement less than 360°.

For example, the carts on a Ferris wheel move along a circle around the center point of that circle. If a cart moves around the wheel once, the angle of rotation is 360°. If the cart was stuck halfway, at the top of the wheel, at that point its angle of rotation was only 180°.

Angles are commonly measured in degrees, radians, gons (gradians) and turns, sometimes also in angular mils and binary radians. They are central to polar coordinates and trigonometry.

## Properties

If the angle of rotation is denoted as AOR,

* $AOR(360a+b)=AOR(b)$ for all integers a and real values b.
