We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…

When an ice cube floating on water in a container melts, it is said in some textbooks that the water level does not change. However, as pointed out by Lan in a recent work, when the buoyant force from a less dense fluid resting above the waterline is taken into account, one should expect a detectable "increase" in the volume of water. Here in this…

Evaporation of a small glass of ethylic alcohol is studied both experimentally and through an elementary thermal physics approach. For a cylindrical beaker and no air flow in the room, a simple quadratic relation is found between the evaporation time and the mass of evaporated liquid. This problem and the obtained results offer excellent…

The ancient Babylonians had an iterative technique for numerically approximating the values of square roots. Their method can be physically implemented using series and parallel resistor networks. A recursive formula for the equivalent resistance R[subscript eq] is developed and converted into a nonrecursive solution for circuits using…

When wave vortices, that is nodal lines of a complex scalar wavefunction in space, approach transversely, their typical crossing and reconnection is a two-stage process incorporating two well-understood elementary events in which locally coplanar hyperbolas switch branches. The explicit description of this reconnection is a pedagogically useful…

The Josephson equations are derived by means of the weakly coupled two-level quantum system model given by Feynman. Adopting a simplified version of Ohta's model, starting from Feynman's model, the strict voltage-frequency Josephson relation is derived. The contribution of Ohta's approach to the comprehension of the additional term given by the…

In this work we discuss the trick of eliminating infinite potential of reference arguing that it corresponds to a constant of integration, in the problem of determining the electrostatic potential of an infinite line of charge with uniform density, and show how the problem must be tackled properly. The usual procedure is confusing for most…

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…

A mathematical derivation of the force exerted by an "inhomogeneous" (i.e. compressible) fluid on the surface of an "arbitrarily shaped" body immersed in it is not found in the literature, which may be attributed to our trust in Archimedes' law of buoyancy. However, this law, also known as Archimedes' principle (AP), does not yield the force…

In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin-orbit-coupling potential is conserved. In a classical nonrelativistic treatment of this problem, in which the Lagrange equations determine the orbital motion and the Thomas equation yields the…

Charges and fields in a straight, infinite, cylindrical wire carrying a steady current are determined in the rest frames of ions and electrons, starting from the standard assumption that the net charge per unit length is zero in the lattice frame and taking into account a self-induced pinch effect. The analysis presented illustrates the mutual…

We have analytically explored the thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials for the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become…

The electrical circuit of the jumping ring experiment based on discharging a capacitor is optimized. The setup is scoop proof at 46 V and yet the ring jumps more than 9 m high. The setup is suitable for both lectures and student laboratory work in higher education. (Contains 1 table, 8 figures and 3 footnotes.)

Linear response laws and causality (the effect cannot precede the cause) are of fundamental importance in physics. In the context of classical electrodynamics, students often have a difficult time grasping these concepts because the physics is obscured by the intermingling of the time and frequency domains. In this paper, we analyse the linear…

The relation M = [mu] x B is presented in all elementary courses on electromagnetism, but it is usually given just for the simple case of a rectangular wire. We will present a completely general but elementary proof of this relation together with two more advanced proof methods. We will then provide some extensions: non-closed wires and…