= Gyroscopic roll torque in a turning vehicle
{title2=$\mathbf G_{\rm body}=-\boldsymbol\Omega\times\mathbf L_f$}
A flywheel's spin <angular momentum> $\mathbf L_f$ must turn with the vehicle. The vehicle supplies <torque> $\boldsymbol\Omega\times\mathbf L_f$ to maintain this <precession>, and experiences the opposite reaction <torque>. With right-handed axes $x$ forward, $y$ left and $z$ up, a left turn has $\boldsymbol\Omega=+\Omega\widehat{\mathbf z}$. A transverse flywheel with $\mathbf L_f=-L_f\widehat{\mathbf y}$ then produces body <torque> $-\Omega L_f\widehat{\mathbf x}$, opposing outward roll. Its magnitude is $L_fv/R_b$ for turn radius $R_b$. Reversing the flywheel reverses the effect.
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