 Smooth equal-disc oblique collision

Let one equal-mass disc arrive with velocity $\mathbf{v}$ while the other is stationary, and let $\mathbf{n}$ be the unit line of centres at contact. A smooth central elastic impulse exchanges their normal velocity components and leaves tangential components unchanged: ${\mathbf{v}}_A^{\prime }=\mathbf{v}-(\mathbf{v}\cdot \mathbf{n})\mathbf{n}$ and ${\mathbf{v}}_B^{\prime }=(\mathbf{v}\cdot \mathbf{n})\mathbf{n}$. The final translational velocities are orthogonal when both are nonzero, and no rotation about a disc centre is generated by the normal impulse. This result concerns nonrelativistic smooth discs; roughness introduces tangential contact dynamics.