Demonstration of the minimal coupling of horizontal accelerations to rotations in a torsion balance suspended from three wires

TL;DR

This study demonstrates that a three-wire torsion balance can effectively minimize coupling of ground tilt and horizontal accelerations to its rotations, enhancing its potential for precise force measurements at small scales.

Contribution

The paper introduces a novel three-wire torsion balance design that exhibits high insensitivity to tilt and horizontal accelerations, with detailed models and experimental validation.

Findings

The three-wire torsion balance is highly insensitive to ground tilt.

Tilt sensitivity is unaffected by shifts in the center of mass.

Static wire lengths primarily determine tilt and acceleration coupling.

Abstract

The Cavendish torsion balance is the instrument of choice for measuring weak forces, such as gravity. Although torsion balances have extremely high sensitivity for measuring forces over ranges of a few cm and more, their dynamics make it difficult to extend this range to much less than fractions of mm. In particular forces such as the Casimir force are usually studied using atomic force microscopes. We present results of our studies of a simple torsion balance with a 3-wire suspension. This device should be able to maintain parallelism between flat plates of areas of a few $\sim\mathrm{cm^2}$ at separations of much less of 10's of $\mathrm{\mu m}$. In this paper we describe our experimental investigation into the coupling of ground tilt to the torsional rotation of the novel device. We show that, like the Cavendish torsion balance, the 3-wire torsion balance is highly insensitive to tilts. We also demonstrate that this tilt sensitivity is itself insensitive to shifts in the centre of mass position of the suspended mass. We discuss simple models of the 3-wire torsion balance that show that it is only the static wire lengths that determine the coupling of tilts and horizontal accelerations. We also discuss designs of torsion balances where sensitivity and noise rejection to tilts are optimised.