Rotationskräfte

Rotationskräfte, or fictitious forces in rotating reference frames, describe accelerations that appear when observing motion from a frame that rotates with angular velocity Ω. They are not real forces in inertial space, but they are convenient terms that allow Newton's laws to be applied in the rotating frame. The main components are the Coriolis force, the centrifugal force, and, when the rotation rate changes, the Euler force.

Mathematically, in a frame rotating with Ω(t), the relation between inertial acceleration a_inertial and the rotating-frame quantities r, v_rot, a_rot is a_inertial = a_rot + 2 Ω × v_rot + Ω × (Ω × r) + dΩ/dt × r. When Newton’s second law is written in the rotating frame, m a_rot = F_real + F_fict, the fictitious forces per unit mass are f_cor = -2 Ω × v_rot, f_cen = -Ω × (Ω × r), and f_E = -(dΩ/dt) × r. These terms account for the observed deflections and accelerations without invoking real forces beyond those acting in the inertial frame.

Applications span meteorology and geophysics (Coriolis effect on winds and ocean currents), engineering and technology (centrifuges and rotating machinery), and demonstrations such as the Foucault pendulum. The Coriolis force explains large-scale weather patterns, while the centrifugal term is central to devices that rely on rotation to generate apparent outward forces. Euler forces become relevant when the rotation rate is not constant.

Rotationskräfte are a tool for describing motion in non-inertial, rotating frames. They do not represent new fundamental interactions but reflect how Newtonian dynamics must be adjusted to account for rotation.