31,570 research outputs found
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
Can a "Hidden Variable'' Quantum Theory Evade the "No-Cloning" Theorem?
If YES, then we can look forward to physical realization of superluminal
communication, as the original considerations of the ``no-cloning'' theorem
were motivated in part as an explanation of why certain schemes for
superluminal signaling cannot work.
If NO, then it would seem that some aspects of the ``hidden'' variables must
be ``intrinsically hidden'', i.e., ``unknowable'', such that
``hidden-variable'' theories belong more to the ``idealist'' than to the
``realist'' school of thought.
I pose this question without proposing a definite answer. I am unaware of any
commentary on this topic during these 23 years since the formulation of the
``no-cloning'' theorem, but I would be pleased to be enlightened by more
knowledgeable readers
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
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