rotasyon

Rotasyon, or rotation, is the motion of a body turning around an internal axis or point, causing a change in orientation without necessarily translating the center of mass. It is a common type of motion in physics, engineering, astronomy, and everyday phenomena.

Kinematic description: angular displacement, ω (angular velocity), and α (angular acceleration) characterize rotation. The axis defines the rotation direction, often determined by the right-hand rule. Orientation is described by how much the object has rotated about the axis.

Mathematical representations: axis-angle, Euler angles, rotation matrices, and quaternions describe rotations. Rotation matrices are orthogonal with determinant 1, preserving distances and angles. Quaternions offer a compact, robust alternative that helps avoid issues like gimbal lock in 3D computations.

Physical implications: angular momentum L = I ω ties rotation to mass distribution through the moment of inertia I. Torque τ changes angular momentum (τ = dL/dt), and in the absence of external torque, angular momentum is conserved. The moment of inertia increases with mass further from the rotation axis.

Applications and examples: many natural bodies rotate, such as the Earth, whose rotation defines day length. In engineering, rotatory systems drive gears and rotors. In computer graphics and robotics, rotations are essential for orienting objects and navigating space, using representations like Euler angles, matrices, or quaternions.