A motion of an object around an axis, described by a set of transformations.Rotation is the motion of an object around an axis, where every point of the object traces a circular path around that line. In physics, it is described by transformations that preserve distances and angles, forming the mathematical group SO(3) in three-dimensional space. Rotation is fundamental to understanding everything from planetary orbits and spinning tops to the behavior of subatomic particles and the structure of spacetime itself.
The formal study of rotation dates back to Leonhard Euler in the 18th century, who established the rotation theorem and the Euler angles. The quantum theory of angular momentum was developed in the 1920s by Wolfgang Pauli and others.
A rotation is characterized by an axis and an angle. Mathematically, it can be represented by a rotation matrix or a quaternion, which transforms coordinates while keeping the origin fixed. In quantum mechanics, rotation is described by angular momentum operators, which obey specific commutation relations and lead to quantized spin states. In general relativity, rotation of massive objects drags spacetime around them, an effect known as frame-dragging.
Rotation is used in gyroscopes for navigation, in the design of rotating machinery, and in particle accelerators where magnetic fields steer charged particles along curved paths.
A neutron star can rotate hundreds of times per second, and its surface moves at a significant fraction of the speed of light.




