Reversion pendulum

Pendulum device with one- second reversion pendulum by Adolf Repsold from 1869, GeoForschungsZentrum , Potsdam

In gravimetry, a reversion pendulum is a pendulum used to measure the acceleration due to gravity . It has two adjustable points or agate cutting edges for suspending and adjusting the adjustable pendulum masses.

The specialty of reversing pendulums is that the two suspension points are set so that they have exactly the same period of oscillation . This avoids the difficult problem of locating the center of gravity of the pendulum in order to accurately determine the pendulum length.

This task is reduced to measuring the distance between the two cutting edges, the value of which is the pendulum length to be entered in the oscillation formula.

With this method, it was already possible to determine the acceleration due to gravity to about a millionth of its value in the 19th century (see Sterneck's pendulum apparatus ). The gravimeters developed around the middle of the 20th century based on the spring balance principle have only achieved this accuracy through a high level of design, calculation methods and reductions , but have now become more precise by a factor of 10 to 100. ${\displaystyle g}$

According to several sources, the reversion pendulum was invented by Johann Gottlieb Friedrich von Bohnenberger . Outside of the German-speaking area, the name Katers Pendel , which refers to the construction of the British physicist Henry Kater from 1817, has largely established itself for the reversion pendulum .

Working principle

Schematic structure of a reversing pendulum

The figure shows the schematic structure of a reversion pendulum with two movable masses.

If the moment of inertia is with respect to the center of gravity of the pendulum, then, according to Steiner's theorem, the moment of inertia with respect to the cutting edge is at a distance from the center of gravity ${\displaystyle J_{S}}$ ${\displaystyle S}$ ${\displaystyle J}$ ${\displaystyle S_{1}}$ ${\displaystyle a}$

${\displaystyle J=J_{S}+m\,a^{2}}$ .

This results in the oscillation period for small deflections

${\displaystyle T_{S_{1}}=2\pi {\sqrt {\frac {J_{S}+m\,a^{2}}{mga}}}}$ .

The same applies to . ${\displaystyle S_{2}}$

If you now determine the positions of the masses in such a way that the periods of oscillation and for oscillations are around or the same, one obtains with (l: reduced pendulum length): ${\displaystyle T_{S_{1}}}$ ${\displaystyle T_{S_{2}}}$ ${\displaystyle S_{1}}$ ${\displaystyle S_{2}}$ ${\displaystyle a+b=l}$

${\displaystyle T_{S_{1}}=T_{S_{2}}=T=2\pi {\sqrt {\frac {l}{g}}}}$ .

Similar considerations apply to reversing pendulums with adjustable cutting edges. If the distance between the cutting edges and the period of oscillation can be measured precisely, then the local acceleration due to gravity and thus the spatial factor can be precisely determined with this experiment .

literature

• Friedrich Georg Wieck, Otto Wilhelm Alund: Naturkrafterna och deras användning (natural forces and their application). 1873-1875, p. 99, website

Web links

• Physics internship RP TU Dresden (PDF; 1200 kB)

Individual evidence

1. ↑ 1997 University of Bonn (PDF; 13 kB)
2. ↑ University of Tübingen
3. ↑ Kater's pendulum, cf. the relevant articles in the foreign-language Wikipedias ( s: , Fri: , nl )