Скачать или смотреть ROTATING FRAME II CORIOLIS FORCE II Derivation 2025

In this lecture, we explore the concept of rotating frames and how motion is described in a non-inertial reference frame. We start by defining an inertial frame S with axes x, y, z and a rotating frame S' with axes x', y', z', rotating with angular velocity Ω. The position vector of a point P, r, remains the same in both frames but its components and unit vectors change. Differentiating r with respect to time leads to the linear velocity in a rotating frame, given by v_space = v_body + Ω × r, where v_body is the velocity in the rotating frame and Ω × r accounts for rotation. Taking the time derivative of velocity, we obtain acceleration in the rotating frame: a_space = a_body + 2 Ω × v_body + Ω × (Ω × r), where the term 2 Ω × v_body represents the Coriolis acceleration and Ω × (Ω × r) represents centripetal acceleration. Applying Newton’s second law in the rotating frame introduces fictitious forces: the Coriolis force (−2 m Ω × v_body) and the centripetal force (−m Ω × (Ω × r)). These forces are essential for understanding the motion of objects in rotating systems, such as the deflection of winds in weather systems, ocean currents, and cyclones. This lecture provides the key equations and concepts needed to analyze motion in non-inertial, rotating frames and highlights the physical significance of the Coriolis and centrifugal effects.
0:00 | Introduction to rotating frames and their importance in physics and meteorology.
1:31 Defining inertial frame S (x, y, z) and rotating frame S' (x', y', z') with angular velocity Ω.
3:01 | Position vector r in both frames and changes in unit vectors after rotation.
5:31 | Time differentiation of r: deriving linear velocity in a rotating frame: v_space = v_body + Ω × r.
8:01 | Time derivative of velocity: acceleration in rotating frame: a_space = a_body + 2 Ω × v_body + Ω × (Ω × r).
10:31 Explanation of Coriolis acceleration (2 Ω × v_body) and centripetal acceleration (Ω × (Ω × r)).
13:01| Applying Newton’s law in rotating frame: fictitious forces – Coriolis force and centrifugal force.
15:31 | Physical significance of Coriolis force in weather systems, ocean currents, and cyclones.
17:01| Summary of key equations and concepts for analyzing motion in non-inertial frames.

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