physics.class-ph

For decades, metrologists have debated heatedly whether a plane angle is a dimensional or dimensionless quantity; whether it is a base quantity in the International System of Units (SI) or a derived quantity. Two main points of view have emerged in the international metrology community. Those who hold the first view believe that a plane angle is a dimensionless derived quantity equal to the ratio of two lengths, and its unit, the radian, is the dimensionless number one (1 rad = 1 m/m = 1). Those who hold the second view believe that a plane angle is a dimensional quantity with its own independent dimension, and its unit, the radian, is not the dimensionless number one, as is currently accepted in the SI. This article demonstrates that, depending on the physical situation, a plane angle is described by either a dimensional or a dimensionless quantity. When measuring, expressing, and communicating an angle's size, physicists use the dimensional quantity plane angle. Its dimension and unit are independent of the dimensions of other quantities and their units. This quantity, plane angle, should be classified as a base quantity, and its unit, radian, should be included in the class of base SI units. In theoretical studies of physical systems with angular quantities, the latter always enter into equations as a dimensionless combination of dimensional plane angles. This dimensionless combination, in turn, is also a physical quantity characterizing the plane angle in question. This new quantity is a dimensionless derived quantity, which physicists also call an angle.

The rotation of the casing and rotor of a gyroscope is studied by considering frictional effects. Friction causes the casing to rotate, and over time, air dissipation and friction at the touchpoint gradually stop this rotation. Several models for air friction, friction between the rotor and casing, and friction at the touchpoint are analyzed. Fit results demonstrate that while some of these models can describe the primary motion, certain effects require further study to yield more precise results. These findings can aid in developing improved models for the rotation of satellites.

We present a complete analytical solution for the stress field inside a homogeneous, inside a homogeneous, linearly elastic solid sphere subjected to a concentrated normal load applied on its surface. Starting from the three-dimensional linearized elastodynamic equations, the displacement and stress fields are derived using scalar and vector potential representations combined with spherical harmonic expansions. All expansion coefficients are determined explicitly by enforcing the traction boundary conditions. The static elastic solution is obtained rigorously as the long-time limit of the dynamical formulation. Closed-form expressions for all components of the stress tensor are provided, enabling direct evaluation of the principal stresses and their differences throughout the interior of the sphere. The analytical solution is further generalized to arbitrary loading positions by means of rotational transformations, allowing systematic treatment of multiple concentrated loads through superposition.

Rotation of conducting and dielectric spherical particles levitating in the uniform electrostatic field is considered. A dipole moment of the spherical particle induced by the external uniform electrostatic field is inclined to the field if the particle rotates. This causes the torque braking the rotation. Vectors of dipole moment and torque depend both on an angular velocity of the particle and its electric properties. Equations of rotary motion of the particle levitating in the external field are integrable in quadratures. Few examples of the conducting and dielectric particles are solved explicitly.

A boundary integral equation (BIE) formulation for 2-D transient elastic wave propagation problems is presented. On the basis of the three-dimensional integral identity, the time-dependent kernels for the two-dimensional boundary integral equation are obtained. A linear time variation of displacements and tractions is assumed over each time step and an implicit time marching scheme is deduced. The formulation is used to obtain an analytical solution for the cylindrical cavity under transient pressure at the boundary surface.

Boundary integral equations are presented to analyze perturbations in terms of small elastic deformations superimposed upon an arbitrary, homogeneous strain. Plane strain deformations of an incompressible, prestressed, anisotropic, elastic solid are considered assuming the Biot constitutive framework. The special case of perturbations of stress/deformation incident wave fields, caused by a shear band of finite length formed inside the material at a certain stage of the deformation path, is formulated.

Newton's Principia is famous for its investigations of the inverse square force law for gravity. But in this book Newton also did something that remained little-known until fairly recently. He figured out what kind of central force exerted upon a particle can rescale its angular velocity by a constant factor without affecting its radial motion. This turns out to be a force obeying an inverse cube law! Here we discuss this and some other interesting features of the inverse cube force law.

The Hahn-Banach Theorem, a cornerstone of modern functional analysis, is a natural companion of the Second Law of Thermodynamics. From a Kelvin-Planck version of the Second Law, the Hahn-Banach Theorem delivers, immediately and simultaneously, entropy and thermodynamic-temperature functions of the local material state such that the Clausius-Duhem inequality is satisfied for every process a particular material might admit. For \emph{existence} of such functions there is no need at all to require that their domain be restricted to states of equilibrium. However, the Hahn-Banach Theorem also indicates that for \emph{uniqueness} of such a pair of functions across the entire state-space domain, every state must be visited by a reversible process. This review is intended to help make accessible to both thermodynamics scholars and mathematicians the remarkable interplay of the Hahn-Banach Theorem and the Second Law.

The Hahn-Banach Theorem, a cornerstone of modern functional analysis, is a natural companion of the Second Law of Thermodynamics. From a Kelvin-Planck version of the Second Law, the Hahn-Banach Theorem delivers, immediately and simultaneously, entropy and thermodynamic-temperature functions of the local material state such that the Clausius-Duhem inequality is satisfied for every process a particular material might admit. For \emph{existence} of such functions there is no need at all to require that their domain be restricted to states of equilibrium. However, the Hahn-Banach Theorem also indicates that for \emph{uniqueness} of such a pair of functions across the entire state-space domain, every state must be visited by a reversible process. This review is intended to help make accessible to both thermodynamics scholars and mathematicians the remarkable interplay of the Hahn-Banach Theorem and the Second Law.

Determination of the electric potential of insulated conducting objects is an important problem both theoretically and practically. For an insulated conducting object in the presence of external charges or charges distributed on the object surface, the problem of potential determination is reformulated using a newly introduced $J$ formalism. Using the $J$ formalism, it is shown how the electric potential can be calculated exactly for spherical objects and efficiently approximated for other object geometries using geometrical properties of the insulated conducting object. This approach does not require calculation of the surface charge distribution at the object surface of the calculation of the electric potential in the surrounding space. Properties and the performance of the approach are investigated numerically using the Robin Hood method. Possible applications of the approach based on the $J$ formalism are outlined for calculation of capacitance of conducting objects.

The linear and nonlinear motions of a damped rigid planar pendulum, driven by vibrating its pivot sinusoidally, are reexamined. The pendulum is known to exhibit periodic, quasiperiodic, and chaotic motions. Floquet analysis identifies regions of instability and stability within the driving parameter space. A new type of nonlinear oscillation may occur at driving parameters where Floquet analysis predicts a stable stationary state. Such non-Floquet oscillations always have periods longer than twice the period of the vibrating pivot. The possible periods of these oscillations may be four, six, eight, or twelve times the driving period. The power spectrum of the pendulum's angular velocity during these oscillations reveals a novel feature: the two dominant response frequencies sum to the driving frequency.

Dynamic room acoustic simulation aims to render the acoustic effects of an environment in real time while accounting for potentially moving sources and receivers. In this context, the efficient synthesis of the long-term room response, also known as late reverberation, remains challenging because of the intricate relationship between room geometry and acoustic behavior. This paper introduces Taylor-SWFT, an efficient implementation of key results from Statistical Wave Field Theory (SWFT) for the geometry-aware dynamic synthesis of late reverberation. The method is evaluated on the Benchmark for Room Acoustical Simulation (BRAS) and achieves competitive performance compared with classical approaches, while substantially reducing computational cost.

We study unidirectional transverse scattering in a two-dimensional acoustic dimer composed of two isotropic subwavelength scatterers. Using a coupled multipole model, we show that inter-particle coupling enables effective monopole-dipole interference and supports a transverse Kerker effect under plane wave excitation. In contrast to a single non-absorbing isotropic particle, where Kerker-type cancellation is only approached in the weak-scattering limit, the dimer can combine pronounced directionality with strong overall scattering. This regime is promising for compact acoustic beam steering and directional wave routing.

Two equal and opposite distributed dead loads are applied orthogonally to the axis of an elastic rod in its rectilinear reference configuration, one at the extrados and the other at the intrados, such that the resultant applied force per unit length is uniformly zero. In this configuration, the rod is subjected to a transverse (tensile or compressive) stress, which is usually believed to have no significant effect on the structural response and has therefore not been considered so far. Contrary to this common belief, the asymptotic behavior of an incrementally deformed elastic layer and three different rod models (the first derived as an asymptotic approximation of the elastic layer; the second based on Euler elastica; and the third obtained by homogenization of a discrete model) reveal that this loading condition produces the same deformation in the rod as an axial load. In particular, the transverse load adds to the axial load in a generalized version of the Euler elastica, leading to buckling and nontrivial postcritical deformations when compressive. The critical transverse stress for buckling is found to have the same form as the Euler critical stress under axial force and tends to zero in the limit of vanishing rod inertia. For this reason, instability induced by transverse loading persists even when the rod thickness tends to zero. These theoretical predictions are confirmed by numerical simulations of a slender elastic layer, which show that increasing transverse load can induce buckling and drive the layer along a deformation path that closely follows that predicted by the generalized Euler elastica throughout the entire postcritical regime, even beyond self-intersection. To show that this behavior can be realized in practice, a dedicated experimental setup is developed, and the experimental results fully confirm the theoretical and numerical predictions.

We investigate the generation of standing waves in the model provided by the inhomogeneous telegraph equation under different forcing conditions. We show that sustained standing waves arise only for a specific forcing that is spatially distributed, continuous, and resonant.

The optical theorem is a powerful tool of scattering theory that directly relates the extinction cross section of a scatterer to its forward scattering amplitude. While widely used in electromagnetism and optics, its application in acoustics has remained limited, primarily due to experimental challenges. These include the finite size of practical sound sources and the stringent requirements for detecting weak scattered signals. In this work, we analyze these limitations and develop a robust methodology for measuring the acoustic extinction cross section under realistic conditions, including non-ideal anechoic environments. The approach is applied to Helmholtz resonators, enabling high-precision measurements even in the presence of pronounced standing-wave resonances. The results demonstrate that, when combined with appropriate data processing, the optical theorem provides a simple and reliable tool for characterizing acoustic resonators, opening new opportunities for quantitative analysis of acoustic scattering and absorption phenomena.

To describe the interactions in magnetically soft particle systems either numerical full-field methods or dipole models are used. Whereas the former are computationally challenging, simple dipole interactions are largely underestimating the actual forces when particles get closer. Based on the full 2-body solution, an analytic approximation scheme for many-body full-field interactions is developed. The concept is formulated in terms of an improved operator that is equivalent to the classical dipole form. The full interaction operator allows to describe cluster formation and dispersion among particles in applied magnetic fields very compactly and highly efficient. In view of its simple 'dipole-like' form, the implementation is straightforward in many areas where magnetically soft objects are used.

The design of contact interfaces that meet quantitatively a specified friction law (friction force vs normal force) is challenging due to the multi-scale and multi-physics nature of contact interactions. Recently, a concept was proposed to address this question in the case of dry elastic microarchitected contact interfaces, so-called metainterfaces. These take their macroscopic friction properties from an array of discrete asperities whose geometrical descriptors are optimized through an inverse design phase. Such design is based on the experimentally-observed proportionality between friction force and real contact area under pure compression, reducing the friction problem to a simpler contact mechanics problem of designing the contact area. In this context, the design strategy assumes that asperities are placed on a linear elastic half-space and behave independently from each other. Both assumptions are likely to fail in experimental realizations of metainterfaces, potentially inducing discrepancies between the actual and target behaviours. Here, we use full 3D finite element modelling to critically assess the validity of those two assumptions in existing experimental metainterfaces, and their potential impact on the design quality. The results first confirm the validity of the strategy, in the conditions in which it was used in the literature. Then, by systematically varying the spatial arrangement of asperities, their interdistance and the size of their elastic base, we identify conditions under which the literature assumptions fail. Our findings provide critical insights into the robustness and practical limitations of the metainterface design strategy and guidelines for its future improvements.

We investigate the gravitational potentials generated by axisymmetric, razor-thin disks. Within certain limitations, the potential on one side of the disk is shown to be equivalent to the potential produced by a linear mass distribution along the axis perpendicular to the disk. We first establish the connection between two mass distributions that generate the same potential. We then consider all disk surface density profiles that produce the potential equivalent to those generated by linear mass distributions, specifically those defined by the elementary beta distribution and its relatives on the interval $[0,1]$, $[1,\infty)$ or $[0,\infty)$. These families of models are important because the potentials in all cases are given by, at most, a single real quadrature of elementary functions of the coordinates, and furthermore, many cases result in closed-form expressions. The potential of many realistic disks may be constructed from some combinations of these disk models.