What is Relative motion; frame in translation, in rotation? — Physics

Definition 18.1 University Physics — Year 1 · Chapter 18 — Non-Inertial Frames; Dynamics on Earth

Let $\mathcal R$ be a frame (origin $O$ ) and $\mathcal R'$ another (origin $O'$ ) moving with respect to it. $\mathcal R'$ is in translation if its axes keep fixed directions in $\mathcal R$ (every point of $\mathcal R'$ has the velocity of $O'$ ); it is in rotation about a fixed axis $\Delta$ if $\Delta$ is fixed in both frames and $\mathcal R'$ turns about it at the angular velocity $\Omega(t)$ . The velocity and acceleration of a point $M$ relative to $\mathcal R'$ , $\vect v'$ and $\vect a'$ , are those a stationary observer of $\mathcal R'$ measures.

Examples

Example 18.3 (Walking on a turntable)

Exercise 11.12 computed the acceleration of a person walking radially at $u$ on a turntable rotating at $\Omega$ : $-ut\Omega^2\vect e_r + 2u\Omega\vect e_\theta$ . In the new language: relative acceleration zero, entrainment $-r\Omega^2\vect e_r$ , Coriolis $2\vect\Omega\wedge u\vect e_r = 2u\Omega\vect e_\theta$ .

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