rotácia

Rotácia, commonly translated as rotation, is the motion of a body around a fixed axis or a fixed point, during which its internal distances remain unchanged while its orientation changes. Rotations can occur in two dimensions, about a single point, or in three dimensions, about a line (the axis). They are contrasted with revolutions, which describe an object orbiting around another body rather than turning about its own axis.

In mathematics, planar rotation by an angle θ about the origin maps coordinates (x, y) to (x cos θ − y sin θ, x sin θ + y cos θ). In three dimensions, rotations are described by an axis and an angle, and can be represented by rotation matrices, quaternions, or the axis–angle form. Angles are often measured in radians or degrees, with radians natural in most calculations.

In physics, rotation is characterized by angular velocity ω, angular momentum L, and moment of inertia I. The linear velocity of a point at distance r from the axis is v = ω × r, and the rotational kinetic energy is (1/2) I ω^2. When no external torque acts, angular momentum is conserved. Rotations can be combined, yielding complex motions described by multiple representations (Euler angles, matrices, or quaternions).

Rotácia occurs across natural and engineered systems. The rotation of Earth underpins day and night and global weather patterns via the Coriolis effect. In technology, rotations are essential in computer graphics, robotics, navigation, and satellite attitude control. Understanding rotation helps in describing celestial mechanics, crystallography, and mechanical design, making it a foundational concept in physics, geometry, and engineering.