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…

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…

The paper is about the appearance of space charge in an ohmic conductor moving in a magnetic field, as pointed out in this journal by Lorrain (1990 "Eur. J. Phys." 11 94-8) and earlier by van Bladel (1973 "Proc. IEEE" 61 260-8). The phenomenon is reinvestigated here in the light of energy balance considerations, in the particular case of a…

We discuss a brief part of a famous paper on sound and light written by Thomas Young in 1800. We show that the proverbial intuition of this famous polymath leads to the discussion of several important and complex fluid dynamics phenomena regarding the behaviour of streams of air. In particular, we show that Young had already explained the adhesion…

In this paper, we revisit, theoretically and experimentally, the fall of a folded U-chain and of a pile-chain. The model calculation implies the division of the whole system into two subsystems of variable mass, allowing us to explore the role of tensional contact forces at the boundary of the subsystems. This justifies, for instance, that the…

A classroom demonstration model has been designed, machined and successfully tested in different learning environments to facilitate understanding of the mechanics of truss structures, in which struts are subject to purely axial load and deformation. Gaining confidence with these structures is crucial for the development of lattice models, which…

With a pedagogical goal, this paper deals with a study of the duration of an elastic collision of an inflatable spherical ball on a planar surface suitable for undergraduate studies. First, the force generated by the deformed spherical ball is obtained under assumptions that are discussed. The study of the motion of the spherical ball colliding…

Resistance to motion often includes a dry frictional term independent of the speed of an object and a fluid drag term varying linearly with speed in the viscous limit. (At higher speeds, quadratic drag can also occur.) Here, measurements are performed for an aluminium disc mounted on bearings that is given an initial twist and allowed to spin…

In the first part of the paper, using a direct calculation two-dimensional motion of a particle sliding on an inclined plane is investigated for general values of friction coefficient ([mu]). A parametric equation for the trajectory of the particle is also obtained. In the second part of the paper, the motion of a sphere on the inclined plane is…

A simple benchtop experiment in which a moving cart collides with a fixed spring is described. Force-time and force-distance data recorded during the collision display the transit of compression wave fronts through the spring following impact. These data can be used by students to develop a computational model of the dynamics of this simple…

Normally, a mechanics laboratory at the undergraduate level includes an experiment to verify compliance with Hooke's law in materials, such as a steel spring and an elastic rubber band. Stress-strain curves are found for these elements. Compression in elastic bands is practically impossible to achieve due to flaccidity. A typical experiment for…

In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary,…

We consider several strategies a paddler may use when paddling a canoe across a flowing river. In particular we look at the case where the paddler keeps their canoe pointed at their chosen destination on the opposite bank of the river. In combination with the downstream flow, the canoe follows a curved path whose shape is determined by a…

A detailed derivation of analytic solutions is presented for overlap, kinetic, nuclear attraction and electron repulsion integrals involving Cartesian Gaussian-type orbitals. It is demonstrated how s-type orbitals can be used to evaluate integrals with higher angular momentum via the properties of Hermite polynomials and differentiation with…