# Yaw from accelerometer? No! So what do these equations actually mean?

note: I'm just a day or so into the use of inertial measurements and trying to learn everything at once, this may be a noob question (it's my first here).

I have seen this image of "Figure 8" in several sites geekmomprojects, makerworkshop, husstechlabs, aros.se, but I don't understand it or how the equations are derived.

If I set an accelerometer on a table so that $a_x$ and $a_y$ are nulled and rotate it around the $\hat{z}$ axis, I'm changing the yaw of the accelerometer but of course there is no change in the value of $\theta$ away from zero as given by the last equation.

So how is this a measurement of yaw? Or am I missing something obvious? What do these three expression actually mean? I'm beginning to think that the first two expressions are simply the "tilt angles" and the third is some geometrical angle that is not actually independent of the other two.

• Thanks. So the first two expressions give what can be called as the "tilt angles" around the $x$ and $y$ axes, correct? My question is really about the equations in this often used image. What does the third expression represent then? – uhoh Sep 26 '17 at 13:18