= Aircraft pitch axis
The \b[aircraft pitch axis] is the transverse body axis about which the nose rotates upward or downward. In the convention used by <NASA Glenn Research Center>, it passes through the <centre of mass> and points toward the right wing tip; the <aircraft roll axis> points toward the nose and the <aircraft yaw axis> toward the underside. These are body-fixed directions, so their orientation relative to the ground changes with the <aircraft>.<Aircraft Rotations by NASA Glenn Research Center>[Pitch axis, Roll axis and Yaw axis]{ref}
Choose right-handed body coordinates $x$ forward, $y$ right and $z$ down. A <force> $\mathbf F$ acting at displacement $\mathbf r$ from the <centre of mass> produces <torque> $\boldsymbol\tau=\mathbf r\times\mathbf F$. Its <pitching moment> is
$$
\tau_y=r_zF_x-r_xF_z.
$$
For an original tail-load example, $\mathbf r=(-4,0,0)\,\mathrm m$ and $\mathbf F=(0,0,100)\,\mathrm N$ give $\tau_y=+400\,\mathrm{N\,m}$. The downward tail load lifts the nose in this convention. If the <aircraft pitch axis> is a principal axis, the motion is initially pure pitch and the corresponding <moment of inertia> is $I_y=2000\,\mathrm{kg\,m^2}$, then the instantaneous <angular acceleration> is $\dot q=\tau_y/I_y=0.20\,\mathrm{rad/s^2}$. Coupled three-axis rotation requires the full <Euler's equations (rigid body dynamics)>.
The axis is a geometrical reference, not necessarily a physical hinge. Changing a control-surface load changes both <forces> and <torques>; a zero net translational <force> does not establish zero <pitching moment>. A balance measurement therefore needs the reference point and sign convention alongside its reported moment.<Aircraft Rotations by NASA Glenn Research Center>[Final control-surface and torque discussion]{ref}
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