摘要:

In this article the virial theorem, which is useful in classical mechanics, quantum mechanics, and statistical mechanics, is considered. Most derivations of this result are of one of two types. Either one starts with the function r⋅p [or operator 1/2 (r⋅p+p⋅r)], or else takes a derivative with respect to the parameter of a scale transformation. It is pointed out that these two methods are closely related, since [r⋅p or 1/2 (r⋅p+p⋅r)]is the generator of scale transformations. This is demonstrated explicitly for classical and quantum‐mechanical systems. The pedagogical advantages in pointing out this connection are also examined.

ISSN:0002-9505    

DOI:10.1119/1.11619

出版商:American Association of Physics Teachers    

年代:1979

数据来源: AIP

摘要:

An experiment investigating the direction of the frictional force exerted by a horizontal surface on a rolling object is discussed. Students generally find the results surprising; however, the observations support the predictions of rotational dynamics. The experiment is suitable for an introductory mechanics laboratory.

ISSN:0002-9505    

DOI:10.1119/1.11620

出版商:American Association of Physics Teachers    

年代:1979

数据来源: AIP

摘要:

A previous discussion of placing a pinhole in front of each eye, and reading with ’’relaxed’’ vision is reconsidered in view of the connection between accommodation and convergence. The increased depth of focus due to the pinholes does not force accommodation to relax. Instead accommodation is free to change without blurring the retinal image. Under these conditions, the accommodative response is dictated, through the accommodative‐convergence relationship, by the convergence demands of the situation.

ISSN:0002-9505    

DOI:10.1119/1.11621

出版商:American Association of Physics Teachers    

年代:1979

数据来源: AIP

摘要:

A method is proposed for illustrating the difference between the Poincaré (inhomogeneous Lorentz) and homogeneous Lorentz groups. Representations of the Poincaré group are constructed from solutions of the relativistic harmonic oscillator equation whose physical wave functions have been effective in describing basic high‐energy hadronic features in the relativistic quark model. It is shown that the Poincaré group can be represented by solutions of the relativistic oscillator equation in a ’’moving cylindrical’’ coordinate system in which the time‐separation variable in the hadronic rest frame is treated separately. Representations which are diagonal in the Casimir operators of the homogeneous Lorentz group are also constructed from solutions of the same oscillator differential equation in a hyperbolic coordinate system. It is pointed out that the difference between the Poincaré and homogeneous Lorentz groups mainfests itself in the coordinate systems in which the oscillator differential equation in separable.

ISSN:0002-9505    

DOI:10.1119/1.11622

出版商:American Association of Physics Teachers    

年代:1979

数据来源: AIP

摘要:

The nonisochronous behavior of a simple pendulum is well known. That this implies a large amount of anharmonicity is a conclusion which seems reasonable to many persons. This paper investigates this matter, and concludes that for all amplitudes the simple pendulum is highly harmonic.

ISSN:0002-9505    

DOI:10.1119/1.11623

出版商:American Association of Physics Teachers    

年代:1979

数据来源: AIP

摘要:

A macroscopic toy of Dirac and Stong shows how to detect 2π rotations in our world. A theorem in geometry shows the toy is maximal; no device in three dimensions can measure bigger angles than this toy. Assuming then that the toy correctly models motion of fermions in our world, a ’’hand waving’’ derivation of the Pauli principle follows. Finally algebra is brought in to express the geometric truth. A famous sign ambiguity goes away.

ISSN:0002-9505    

DOI:10.1119/1.11635

出版商:American Association of Physics Teachers    

年代:1979

数据来源: AIP

摘要:

By numeric integration of the dynamic equations of motion for linear elastic collisions we show that the final velocities are different from those traditionally expected. Both air‐track glider and compressible sphere collisions were modeled. Final velocities in all cases were independent of the force constants of the separating springs and the compressibility of the spheres. Experimental measurements of the final velocities for three body collisions of similar air‐track gliders and of similar elastic spheres are presented which agree well with the calculations.

ISSN:0002-9505    

DOI:10.1119/1.11636

出版商:American Association of Physics Teachers    

年代:1979

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.11637

出版商:American Association of Physics Teachers    

年代:1979

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.11638

出版商:American Association of Physics Teachers    

年代:1979

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.11639

出版商:American Association of Physics Teachers    

年代:1979

数据来源: AIP