We tested the gravitational 1/r 2 law using a stationary torsion-balance detector and a rotating attractor containing test bodies with both 18-fold and 120-fold azimuthal symmetries that simultaneously tests the 1/r 2 law at two different length scales. We took data at detector-attractor separations between 52 µm and 3.0 mm. Newtonian gravity gave an excellent fit to our data, limiting with 95% confidence any gravitational-strength Yukawa interactions to ranges < 38.6 µm.

We used a torsion pendulum and rotating attractor with 20-pole electron-spin distributions to probe dipole-dipole interactions mediated by exotic pseudo-Goldstone bosons with m b ≤ 500 µeV and coupling strengths up to 14 orders of magnitude weaker than electromagnetism. This corresponds to symmetry-breaking scales F ≤ 70 TeV, the highest reached in any laboratory experiment. We used an attractor with a 20-pole unpolarized mass distribution to improve laboratory bounds on CP -violating monopole-dipole interactions with 1.5 µeV< m b < 400 µeV by a factor of up to 1000.

We describe a torsion pendulum with a large mass-quadrupole moment and a resonant frequency of 2.8 mHz, whose angle is measured using a Michelson interferometer. The system achieved noise levels of ∼200prad/Hz between 0.2 and 30 Hz and ∼10prad/Hz above 100 Hz. Such a system can be applied to a broad range of fields from the study of rotational seismic motion and elastogravity signals to gravitational wave observation and tests of gravity.

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Two Eöt–Wash torsion balance instruments exploited optimized Fourier–Bessel geometries to test the short-distance properties of gravity and to constrain exotic dipole–dipole and monopole–dipole interactions. We discuss efficient analytic techniques for computing the expected torques in those instruments arising from Newtonian and Yukawa interactions between unpolarized test bodies and dipole–dipole and monopole–dipole torques on polarized test-bodies. We consider systematic effects induced by weak external magnetic fields on the nominally unpolarized test-bodies. We also present a new Fourier–Bessel expansion for inverse-power-law (IPL) potentials and use this to calculate the expected IPL signals in our recent short-distance test of the gravitational inverse-square law. Our results slightly improve limits on inverse-5th-power law potentials.

We correct errors in seven of the more than 100 expressions for the gravitational inner spherical multipole moments of several homogeneous solids. No additional corrections have been found.