Four-acceleration in uniform circular motion
= Four-acceleration in uniform circular motion
{title2=$\sqrt{-A_\mu A^\mu}=\gamma^2v^2/r$}
For uniform <circular motion> in an inertial laboratory, the <Lorentz factor> is constant. With <metric signature> $+---$, <four-acceleration> is $A^\mu=(0,\gamma^2\mathbf a)$ and <proper acceleration> has magnitude $\gamma^2v^2/r$. The instantaneous spatial <acceleration> is perpendicular to <velocity>, even though the particle has nonzero <proper acceleration>.