Editing Circular motion (section)

==== Relativistic circular motion ====

In this case, the three-acceleration vector is perpendicular to the three-velocity vector, 
<math display="block">\mathbf{u} \cdot \mathbf{a} = 0. </math>
and the square of proper acceleration, expressed as a scalar invariant, the same in all reference frames,
<math display="block">\alpha^2 = \gamma^4 a^2 + \gamma^6 \left(\mathbf{u} \cdot \mathbf{a}\right)^2/c^2, </math>
becomes the expression for circular motion, 
<math display="block">\alpha^2 = \gamma^4 a^2. </math>
or, taking the positive square root and using the three-acceleration, we arrive at the proper acceleration for circular motion: 
<math display="block">\alpha = \gamma^2 \frac{v^2}{r}. </math>