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I have a body and the reference frames, one is the inertial reference frame O-xyz, the other is a non inertial reference frame O'-x'y'z' fixed on the body. The angular velocity vector of the body observed in the inertial reference frame is $\overrightarrow{\omega}_{Inertial}$.

Is the angular velocity vector $\overrightarrow{\omega}_{Non-Inertial}$ of the body observed in the non inertial reference frame equal to zero? If I observe a point of the body when I am fixed on the body, I will see that point fixed, so it has not an angular velocity in the non inertial reference frame. Is this right?

Thank you so much in advance.

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    $\begingroup$ I think so. Since the definition for angular velocity is just $\vec{r} \times \vec{v}$, and $\vec{v}$ relative to that ref. point fixed on and coming with the body is just zero, no matter it is inertial or not. $\endgroup$
    – pinchun
    Commented Feb 7, 2019 at 10:16
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    $\begingroup$ Yes, it is zero $\endgroup$
    – Digiproc
    Commented Feb 7, 2019 at 10:45

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When you are sitting still on a rotating merry-go-round / the Earth you are not rotating relative to the merry-go-round / the Earth.

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Your question, if taken literally, has an obvious answer, i.e. zero. But this raised a doubt: perhaps you were thinking of a somewhat different thing. In theory of rigid motions it's usual to refer the angular velocity (wrt a "fixed" frame) to axes fixed to the body. At least in italian tradition the angular velocity components referred to the principal axes of inertia are called $p$, $q$, $r$.

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  • $\begingroup$ Hello @ElioFabri, thank you for the clarification. I was confusing because in biomechanics we use a lot notations to specify each physical quantity, instead in mechanics books there is little care for the notations. Now I unsterstood the notations of the book $\endgroup$
    – Gennaro Arguzzi
    Commented Feb 8, 2019 at 16:18

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