The Rolling Motion of a Disk on a Horizontal Plane

Recent interest in the old problem of the motion of a coin spinning on a tabletop has focused on mechanisms of dissipation of energy as the angle alpha of the coin to the table decreases, while the angular velocity Omega of the point of contact increases. Following a review of the general equations of motion of a thin disk rolling without slipping on a horizontal surface, we present results of simple experiment on the time dependence of the motion that indicate the dominant dissipative power loss to be proportional to the Omega^2 up to and including the last observable cycle.Comment: v2 adds experimental data on the role of friction at small angles, and adds several references. Thanks to A. Chatterjee, C. Gray and A. Ruina v3 adds discussion of the case of zero friction; thanks to Martin Olsso

Circular Orbits Inside the Sphere of Death

A wheel or sphere rolling without slipping on the inside of a sphere in a uniform gravitational field can have stable circular orbits that lie wholly above the "equator", while a particle sliding freely cannot.Comment: Figures revised slightly since publicatio

Radiation from a Superluminal Source

The sweep speed of an electron beam across the face of an oscilloscope can exceed the velocity of light, although of course the velocity of the electrons does not. Associated with this possibility there should be a kind of Cherenkov radiation, as if the oscilloscope trace were due to a charge moving with superluminal velocity

Axicon Gaussian Laser Beams

We deduce the simplest form for an axicon Gaussian laser beam, i.e., one with radial polarization of the electric field.Comment: v2 adds one figure and one referenc

Magnetostatic Spin Waves

In general, Maxwell's equations require that a wave of magnetic field be accompanied by a wave of electric field, and vice versa. In magnetic media it is possible to have waves of magnetization with negligible electric field. We discuss an example of this based on ferromagnetic spin waves.Comment: 7 pages, no figure

The Hawking-Unruh Temperature and Quantum Fluctuations in Particle Accelerators

We wish to draw attention to a novel view of the effect of the quantum fluctuations during the radiation of accelerated particles, particularly those in storage rings. This view is inspired by the remarkable insight of Hawking that the effect of the strong gravitational field of a black hole on the quantum fluctuations of the surrounding space is to cause the black hole to radiate with a temperature T = hbar g / 2 pi c k, where g is the acceleration due to gravity at the surface of the black hole, c is the speed of light, and k is Boltzmann's constant. Shortly thereafter Unruh argued that an accelerated observer should become excited by quantum fluctuations to a temperature T = hbar a* / 2 pi c k, where a* is the acceleration of the observer in its instantaneous rest frame. In a series of papers Bell and co-workers have noted that electron storage rings provide a demonstration of the utility of the Hawking-Unruh temperature, with emphasis on the question of the incomplete polarization of the electrons due to quantum fluctuations of synchrotron radiation. Here we expand slightly on the results of Bell et al., and encourage the reader to consult the literature for more detailed understanding

Maximal Gravity at the Surface of an Asteroid

The maximum strength of gravity at the surface of an object of a given mass is not attained for a spherical shape, but for a small departure from sphericity.Comment: 4 pages, 1 figur

An Electrostatic Wave

In general, Maxwell's equations require that a wave of electric field be accompanied by a wave of magnetic field, and vice versa. However, it is possible to have a plane wave in a dielectric medium with electric field E parallel to the wave vector k (a longitudinal wave) with no time-dependent magnetic field provided the electric displacement D is zero. We give an example from plasma physics: the so-called Bernstein wave.Comment: 8 pages, no figure

A Strategy for Accelerator-Based Neutrino Physics in the USA

We outline a strategy for next-generation neutrino physics experiments based on beams from accelerators in North America. This strategy is based on the mounting evidence in favor of the large mixing angle solution to solar neutrino problem, which implies that in addition to measurement of sin^2 2theta_13 and of the sign of Delta m^2_23, measurement of CP violation in the neutrino sector is a realizable goal if sin^2 2theta_13 is not too small. The strategy is to begin with a new detector, 20-30 kton of liquid argon, designed to make best use of the NUMI beam currently under construction at FNAL. Then, after new measurements have made the optimal path clearer, we anticipate choosing among options for neutrino "superbeam" upgrades at BNL and/or FNAL as well as for second new detector of 100-200 kton.Comment: v2 has an updated Fig. 3, thanks to Debbie Harris. Thanks also to Bob Shroc

An Off-Axis Neutrino Beam

In this pedagogic note, set as problem for the reader, it is shown how the existence of a maximum energy of a neutrino that appears at a given angle to the direction of its parent pion leads to a useful enhancment of neutrino flux in an off-axis beam