What Is Rotation?
A transformation that turns a shape around a fixed point called the centre of rotation, through a specified angle and in a specified direction (clockwise or anticlockwise).
Imagine placing your finger on a point on a piece of paper and then spinning the paper around that finger. Every point on the paper traces out a circular arc — that's exactly what rotation does to a geometrical shape.
Three pieces of information fully describe any rotation:
- Centre of rotation — the fixed point the shape rotates around
- Angle of rotation — how far the shape turns (measured in degrees)
- Direction of rotation — clockwise (CW) or anticlockwise (ACW, sometimes called counterclockwise)
Think of a clock's hands. The centre of the clock is the centre of rotation. The minute hand rotates every hour in a clockwise direction. If you watched the clock in a mirror, it would appear to move anticlockwise.
Why does this matter in Science? Rotation is everywhere in the natural and engineered world — from the spinning of gears in machines, to the rotation of molecules that determines how substances interact, to the orbit of planets and the symmetry of crystals. Understanding rotation gives you a powerful tool for analysing spatial patterns in science.
Key Vocabulary
The fixed point around which a shape is rotated. It can be inside, on the edge of, or outside the shape.
The number of degrees through which every point of the shape is turned around the centre of rotation. Common angles include , , , and .
The new position of a shape after a transformation has been applied. We often label the image with a prime symbol, e.g., if the original point is , its image is .
The original shape before the transformation is applied.
A transformation that preserves all distances and angles, keeping the shape and size identical. The image is always congruent to the pre-image.
Rotation is an isometric transformation — it preserves the size and shape of the figure. The image is always congruent to the pre-image.
15 more sections in this topic
Pick this up in your Library: it holds the whole topic, notes, cheatsheet and questions.