# Angular velocity of a body observed from a frame of reference fixed on the body

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.

• 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. – pinchun Feb 7 at 10:16
• Yes, it is zero – Digiproc Feb 7 at 10:45

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 $$p$$, $$q$$, $$r$$.