Welcome to the American Journal of Physics (AJP). AJP publishes papers that meet the needs and intellectual interests of college and university physics teachers and students. This Journal was established in 1933 under the title the American Physics Teacher, which covers Volumes 1 through 7. The name was changed to the American Journal of Physics in 1940.
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We use the variational principle to obtain the wave functions of elliptical quantum dots under the influence of an external magnetic field. For the first excited states, whose wave functions have recently been mapped experimentally, we find a simple expression, based on a linear combination of the wave functions in the absence of a magnetic field. The results illustrate how a magnetic field breaks the xy symmetry and mixes the corresponding eigenstates. The obtained eigenenergies agree well with those obtained by more involved analytical and numerical methods.

The spin of a gyroscope that undergoes Thomas precession seems to change its direction without any torque, which would mean that conservation of angular momentum is violated. To resolve this paradox, it is shown that the spin dynamics equation describing Thomas precession (the BMT equation) can be written in terms of a torque applied to the spin. A simple method of finding an explicit expression for the torque is presented in the case of a gyroscope performing circular motion. An unexpected oscillatory character of the torque is explained in terms of the difference between the proper spin and the spin observed in the laboratory frame.

Physics students now have access to interactive molecular dynamics simulations that can model and animate the motions of hundreds of particles, such as noble gas atoms, that attract each other weakly at short distances but repel strongly when pressed together. Using these simulations, students can develop an understanding of forces and motions at the molecular scale, nonideal fluids, phases of matter, thermal equilibrium, nonequilibrium states, the Boltzmann distribution, the arrow of time, and much more. This article summarizes the basic features and capabilities of such a simulation, presents a variety of student exercises using it at the introductory and intermediate levels, and describes some enhancements that can further extend its uses. A working simulation code, in html5 and javascript for running within any modern Web browser, is provided as an online supplement.

We derive the rotational form of Newton's second law from the translational form by performing a force analysis of a simple body consisting of two discrete masses. Curiously, a truly rigid body model leads to an incorrect statement of the rotational second law. The failure of this model is traced to its violation of the strong form of Newton's third law. This leads us to consider a slightly modified nonrigid model that respects the third law, produces the correct rotational second law, and makes explicit the importance of the product of the tangential force with the radial distance: the torque.

We consider the onedimensional scattering of two identical blocks of mass M that exchange energy and momentum via elastic collisions with an intermediary ball of mass . Initially, one block is incident upon the ball with the other block at rest. For , the three objects will make multiple collisions with one another. In our analysis, we construct a Euclidean vector whose components are proportional to the velocities of the objects. Energymomentum conservation then requires a covariant recurrence relation for that transforms like a pure rotation in three dimensions. The analytic solutions of the terminal velocities result in a remarkable prediction for values of α, in cases where the initial energy and momentum of the incident block are completely transferred to the scattered block. We call these values for α “magic mass ratios.”