The top 500 results for "spin" are:

Measurements are presented on the rise of a spinning egg. It was found that the spin, the angular momentum and the kinetic energy all decrease as the egg rises, unlike the case of a ballerina who can increase her spin and kinetic energy by reducing her moment of inertia. The observed effects can be explained, in part, in terms of rolling friction between the egg and the surface on which it spins.

It is shown that quaternions offer a simple elegant description of spin of a single particle, perhaps superior to that of conventional quantum mechanics. The spin operators are S_x=¹/₂i, S_y=¹/₂j and S_z=¹/₂k (in units where h(cross)=1). Quaternion angular functions Z_j^+or-, m_j are given, which are explicit expressions for mod l,s,j,m_j> in terms of the states mod l,s,m_l,m_s>. Use of these Z^+or- functions offer an elegant analysis of: (i) the relativistic hydrogen atom; (ii) problems in classical physics, such as the wave equation (in which 'spin' emerges as a feature of the mathematics). Consideration is given to a speculation that there is simultaneous 'reality' of all three components of spin. The quaternion quantum mechanical arguments developed here are not incompatible with the results of a recent experiment on phase change commutivity by Kaiser. George and Werner (1984).

We review the literature on the Pauli equation and its current density, discussing the progression from the original phenomenological version of Pauli to its derivation by Lévy-Leblond from a linearization of the Schrödinger equation. It was established conclusively by Lévy-Leblond's  work that the spin of a spin-1/2 particle such as an electron is non-relativistic in nature, contrary to what was often stated following Dirac's derivation of a relativistic wave equation, and his subsequent demonstration that Pauli's spin interaction term appeared in the non-relativistic limit. In this limit, the Gordon decomposition of the associated probability current density was found to contain a spin-dependent term. Such a term does not follow, however, from the usual derivation of the current density from the Pauli equation, although various physically motivated but otherwise ad hoc explanations were put forward to account for it. We comment on the only exception to these of which we are aware implying the spin term in the current was in fact non-relativistic in nature. However, the earlier work of Lévy-Leblond had already shown, with no additional assumptions, that this term was a prominent feature of the current density derived from his equation. Hence, just as with the spin itself, the spin current was non-relativistic, claims to the contrary notwithstanding. We present a somewhat simplified derivation of the Lévy-Leblond equation and its current density, commenting on possibilities for experimental work that might indicate measurable consequences of the spin term in the current density. The presentation is at a level of quantum mechanics, electromagnetic theory, and mathematical methods typical of courses taken by first-year graduate students in physics, assuming some familiarity with Pauli spin matrices and the Dirac equation. Calculations are presented in detail, making the material suitable for use by teachers as supplementary problems for assignments, and development of theoretical concepts peculiar to the Pauli equation and its probability current density.

Strobe photographs of a spinning, bouncing `superball' are analysed to determine whether observed reversals of spin during bouncing fit a model analogous to Newton's experimental law of restitution. Rough, but imperfect agreement is found.

We characterize and classify the quantum states of a pair of spin-½ particles in terms of the entanglement of the pair. We describe a general strategy for classifying the quantum states of entangled systems, and apply it to the simplest entangled system available - a pair of spin-½ particles. The method is based on local unitary transformations. We give a set of six parameters that describe an arbitrary pure state of a pair of spins, one of which is the entanglement of the pair. We discuss visual representations of the state of this system, and propose a visualization using a Bloch sphere for each subsystem and a disc to record the `shared' information.

We analyze idealized sequential Stern–Gerlach (SG) experiments with higher spin particles. This analysis serves at least two purposes: the widely discussed spin-1/2 case leads to some misunderstandings since the probabilities are always evenly distributed for the sequential orthogonal magnets, which does not generalize to higher spins. A detailed discussion of the higher spin case, as is done here, is highly useful. Secondly, the Wigner rotation matrices for generic spins become conceptually more transparent with this physical example. We also give compact formulas for the probabilities in terms of the angle between the sequential SG apparatus for generic spins. We work out the spin-1/2, spin-1 cases explicitly. Since there are some confusing issues regarding the actual experiment, we also compile a 'facts and fiction' section on the SG experiments.

It is suggested that a thorough treatment of electron spin has advantages as a method of presenting many of the concepts and techniques of intermediate quantum mechanics. The starting point is the Stern-Gerlach experiment, from which the anticommutation relations for the spin operators may immediately be deduced. The commutation relations, which demonstrate that the spin is an angular momentum, are derived from these and it is shown that the anomalous gyromagnetic ratio is a natural consequence of the properties of the spin operators. The Pauli theory, which is the simplest example of the use of matrices in quantum mechanics, is briefly summarised, and employed in an analysis of the double Stern-Gerlach experiment. This example of a change of representation is used to introduce Dirac's transformation theory which, together with a variant of the double Stern-Gerlach experiment, is made use of in a discussion of the EPR paradox, Bell's inequality and hidden-variable theories. It is emphasised that the quantum mechanical description of these phenomena is consistent and that, from the viewpoint of quantum theory, no action-at-a-distance is required to explain them.

Based on a geometric view on the famous Dirac belt trick in terms of a Möbius strip, we propose a simple haptic model for spin states as standing waves in non-trivial geometry. We compare two representations of the model: the spinor representation in SU(2), which geometrically is described by 'Dirac belt' states on S₃, and the well-known Bloch-sphere representation on S₂. We show that after Hopf-mapping ${S}_{3}\to {S}_{2}$, the position and number of nodal points are sufficient to describe the spin state and make the relation between the representations on S₂ and on S₃ explicit in simple haptic models. Our approach is well-suited for graduate physics courses, and provides a thorough understanding of the complex geometry of spin states beyond the usual Bloch-sphere visualisation. It turns out that an even number 2l of nodal points can be related to nodal lines of spherical harmonics Y_lm, an odd number can be traced back to spin states. In this sense, our model provides a unified view for orbital and spin states based on a simple picture of standing waves.

Two simple cases and a special case are studied for the gyroscope. The time evolution of the angular velocities is analyzed. It can be seen that nutation affects spin angular velocity and the numerical solutions for the special case show that the gyroscope can reverse its spin direction. This is the result of the conservation of angular momenta and this work can be used to teach its role in such cases.

A conventional tippe top consists of a hollow, truncated sphere with a short peg at the top so that the top can easily be spun between the thumb and index finger of one hand. A simpler version is described in the present paper, consisting only of a hemispherical shell. When spun about a vertical axis at moderate speed, the shell rises and completely inverts. A hemispherical shell therefore acts in the same way as a conventional tippe top, but with two main differences. One is that it spins in the opposite direction about its axis of symmetry. The other is that it precesses on its rim after inversion, in a manner similar to a spinning disk.