rotationally

Rotationally is an adverb describing something that is done by rotating around an axis, or a property of a system that involves rotation. In everyday use, it characterizes actions or phenomena that occur through rotation rather than translation or static orientation.

In physics and geometry, rotational motion involves angular variables such as angular velocity, angular acceleration, and torque. A rotating body has angular momentum L and rotational kinetic energy (1/2) I ω^2, where I is the moment of inertia and ω is the angular velocity. Quantities can be described as rotationally invariant if they do not change under a rotation, and a system may be said to possess rotational symmetry when its description is unchanged by certain rotations. The mathematics of rotations is formalized through rotation operators and the rotation group SO(3), which act on vectors and tensors.

Rotational concepts have wide applications. Rotational spectroscopy studies transitions between rotational energy levels in molecules, revealing information about molecular structure and moments of inertia. In astronomy, the rotation of stars and galaxies influences observed spectra and dynamics. In crystallography and materials science, rotational symmetry helps classify crystal classes and informs properties such as diffraction patterns. In engineering, devices often convert between linear and rotational motion, and notions of rotationally invariant quantities underpin design and analysis of rotating machinery.

Overall, rotationally describes processes and properties tied to rotation about an axis, distinguishing them from purely translational or orbital phenomena and enabling a specific set of mathematical tools for analysis.