= Rotating-wheel molecular velocity selector
<Otto Stern>'s lecture describes two co-rotating toothed wheels: transit between them must match an advance between openings. He explicitly distinguishes this method from the first historical speed measurement.<The Method of Molecular Rays by Otto Stern>[The method of molecular rays, lecture 12 December 1946, p. 9: rotating-wheel timing, transmission and limited accuracy]{ref}
For an idealized example, let aligned wheels have $N$ equally spaced openings, separation $L$, and rotation rate $f$ in revolutions per second. A particle with constant longitudinal <speed> $v$ takes $L/v$ between them. The second wheel advances through $fL/v$ revolutions; transmission peaks when that advance is an integer number $k$ of opening pitches:
$$
\boxed{v_k=\frac{NfL}{k}},\qquad k=1,2,\ldots.
$$
With chosen $N=60$, $f=50\,\mathrm{Hz}$ and $L=0.080\,\mathrm m$, the first two orders select $240$ and $120\,\mathrm{m\,s^{-1}}$. A second transmission maximum therefore need not represent a second source <temperature>. Finite opening widths admit speed intervals around each order, and an additional measurement is needed to distinguish orders. The ideal expression assumes negligible <acceleration> and constant rotation rate during a flight, with a fixed relative phase between the wheels.
Back to article page
