Rotation

Rotation is the movement of an object where at least one point stays in the same place. In two dimensions, like flat pictures, a shape can turn either clockwise or counterclockwise around a point known as the center of rotation. This is how a wheel turns or how a merry-go-round spins.

In three dimensions, solid objects like planets or toys rotate around an imaginary line called an axis of rotation. For example, when the Earth turns, it spins around an axis that goes through its center. This spin defines points on the Earth called geographical poles.

There are two main types of rotation. One type, called a spin, happens when an object rotates around an axis that passes through its own center of mass. The other type, called a revolution or orbit, happens when an object rotates around an axis outside of itself, like the Earth moving around the Sun. Both types of rotation are linked to ideas in physics such as angular velocity and angular momentum, which help describe how fast and how objects move when they turn.

Mathematics

A rotation is a way of moving that keeps at least one point in the same place. In two dimensions, this means turning around one point. In three dimensions, objects can turn around an imaginary line called an axis of rotation.

All movements of solid objects, like things that don’t bend or change shape, are either rotations, translations (sliding without turning), or a mix of both. A rotation is like turning something around a center point. If you turn something twice around the same point or axis, you get a new rotation. Rotations around the x, y, and z axes are called principal rotations, and any rotation can be split into these three types.

Physics

The speed of rotation can be measured in different ways, such as using angular frequency. This tells us how fast something spins. When an object spins, it can also speed up or slow down. This change is called angular acceleration. It happens because of a force called torque.

In physics, the way an object spins can be described using special directions. For example, the direction an object spins around can be shown using the right-hand rule. This is similar to how a screw moves.

Rotation is different from circular motion. In circular motion, an object moves in a circle but doesn’t change its own direction. In rotation, the object’s direction does change. This change can be described as spinning around an imaginary line called an axis.

Astronomy

In astronomy, rotation is something we see often. It includes the spinning of objects, called auto-rotation, and their movement around other objects, called orbital revolution.

Stars, planets, and other space objects can spin around their own centers. For example, the planets in our Solar System were first seen by watching marks on their surfaces. We study the Sun's rotation by watching sunspots, which move with the Sun's outer layers.

Most planets spin in the same direction they move around the Sun, but Venus and Uranus are different. Venus spins slowly backward, while Uranus spins almost on its side. Moons move around their planets, and planets move around stars, like Earth around the Sun. Stars also move slowly around the centers of their galaxies.

Applied

Main article: Aircraft principal axes

In flight dynamics, rotation helps explain how airplanes move. Planes can tilt up and down, called pitch, tilt side to side, called roll, or turn left and right, called yaw. These movements help pilots steer the airplane.

Rotation is also useful in sports and amusement rides. In sports like tennis, players spin the ball to change how it moves. Amusement rides like Ferris wheels and carousels use rotation to create fun. Rides such as Chair-O-Planes and roller coasters use rotation to make the experience exciting and keep people safe.