# rotation

Figure 1.

Figure 2.

## Rotation in physics

In physics, rotation is the turning or spinning of a body, such as a planet, star, or galaxy, about an axis running through it.

### Rotation period

The rotation period of an object is the time taken for one complete turn (through 360 degrees) round the object's axis of rotation.

## Rotation in mathematics

In mathematics, rotation is a transformation in which a figure turns through a specific angle about a fixed point,
called the **center of rotation**. The center of rotation
may be inside or outside the figure that is being transformed. If the
figure is turned anticlockwise, the rotation is considered positive,
while a negative rotation turns the figure clockwise.

### Rotations in a plane

The rotations in a plane are determined by the point *P* in the plane which is unaltered by the rotation (center of rotation), and by the angle of rotation *φ*.

The image point *A*_{1} of a given point *A* can be constructed as follows. A circle with radius *PA* is described about *P* and the angle *φ* constructed on *PA* with vertex *P*. The intersection of the free arm of *φ* and the circle is the required image point *A*_{1} (see Figure 1).

*Example*: Rotation of a triangle *ABC* about its vertex *A* through angle *φ* = 360°. The image of the triangle is *AB*_{1}*C*_{1} (see Figure 2).

## Rotations in space

A rotation in space is determined when an axis of rotation and an angle of rotation are given.