The Physics Educator

A novel use of the LiDAR sensor of a smartphone spring in introductory physics experiments is discussed in this paper. We have determined the spring constant for various combinations of springs using the LiDAR sensor of a smartphone through the phyphox application. An electrical heater coil is used as a spring, and the period of oscillation of a vertical spring–mass system is measured using a LiDAR sensor. The experimental values of spring constants agree with the theoretical values. A high school student can perform this simple experiment in a smart way at home.

Theoretical analysis of sliding ladder on a stationary and freely moving wall is presented. The equation of motion and kinematic variables have been derived using Newton’s law and conservation of mechanical energy without calculus. We also plot several kinematic variables versus the angle formed by the ladder and wall. Moreover, we determine the last contact angle at which the ladder loses contact with the wall. This paper investigates four cases of sliding ladder which will be useful for undergraduate students in understanding rotational dynamics.

We describe the essence of the so-called “alignment effect” from the standpoint of the maximum power principle and consider the main features of this effect within the framework of the relativistic approach. The paper is addressed to undergraduates studying the basics of the special theory of relativity.

This research aims to give a comparison between classical mechanics and special relativity in term of formulating central force. We derive the Binet equation in relativistic form and find its solution. Then, we discuss the stability of the orbit and make several plots as well as the comparisons of kinematics variables by taking specific example namely circular orbit. Finally, we investigate the relativistic effect in Rutherford scattering by considering some variables including the closest distance and deflection angle. We believe this paper provides a good example for students about the difference between relativistic and classical central force.

In this paper, we address the nonlinear dynamics of Dzhanibekov’s dancing wing nut and the related intermediate axes theorem governing the motion of a tossed tennis racket. Drawing first on the comprehensive investigations by Murakami, Rios and Impelluso [J. Appl. Mech. 83 (2016), doi:10.1115/1.4034318] we extend the exploration of the wing nut’s spherical phase portrait by incorporating basins of attraction and their heteroclinic connections. We then turn our attention to the significant damping studies of Español, Thachuk and de la Torre [Eur. J. Mech. A Solids 103, 105184 (2024)] who derive from first principles a generalized stochastic version of the Euler equations which can incorporate both oriental realignment (which they call oriental diffusion) and viscoelastic effects. Applied to the wing nut dancing, they showed that the former is the more significant effect and as the authors say “Had Dzhanibekov observed his wing nut for a sufficiently long period, he would have found it spinning around the major axis. In other words, precession relaxation kills the Dzhanibekov effect in the long run.”

We solve the infinite-potential well problem using the method of Heisenberg’s matrix mechanics. In addition to being of educational value, the matrix mechanics allows us to deal with various unphysical issues caused by this potential in a seemingly unproblematic fashion. We also show how to treat many particles within this representation.