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Describes a method for measuring the radius of gyration of a sphere and a barrel. Scientific concepts relevant to the determination of a circular object's radius of gyration, including conservation of energy; Significance of measuring the radius of gyration of an object in the study of rotational motion; Measurements of the radius of gyration of a sphere and a barrel.

The authors investigate by simulation the Coulomb effects on brightness and energy spread for cold field emitters. At first, we show that brightness is ultimately limited by Coulomb interactions. The authors analyze the maximum attainable brightness for tip radii ranging from 1 nm to 1 μm. Remarkably, the brightness of a tip of 1 nm is comparable to a tip of 1 μm. Higher brightness can be achieved by adding a plate at the base of the field emitter, and therefore decreasing the shank length. However, the brightness enhancement due to the protrusion is ultimately limited by large extractor voltages and increased energy spread. In particular, the energy spread for larger tip radii grows faster with brightness. The authors conclude that performance enhancement due to the protrusion works best for smaller tip radii. [ABSTRACT FROM AUTHOR]

The concept of areal velocity is intrinsically and historically connected with that of angular momentum. For central force fields the area swept out in the orbital plane by a particle's radius vector is proportional to the time. For non-planar problems, it is shown that a particle's position vector sweeps out a general conical surface and that interesting kinematical relations hold. The areal velocity vector is always perpendicular to the conical surface and is proportional to the angular momentum of the particle. In some problems, the magnitude of the areal velocity is constant while its direction changes. In others, only a component of the areal velocity vector is constant. A moving orthonormal basis associated with the areal velocity is defined and a matrix equation for the angular velocities of the basis vectors is found to have an elegant form, involving ‘sweeping’ and ‘tilting’ components. Illustrative examples are provided and some historical background is included. [ABSTRACT FROM AUTHOR]

Discusses a physics experiment on the use of a spread-sheet simulation for artificial satellites orbiting through an atmosphere of variable density. Equation used to calculate the value of the satellite's energy at the end of the orbit and determine the orbital radius and speed corresponding to that energy; Importance of the completion of a concept map worksheet by students; Goals of the activity.

We revisit a recent analysis of the time of fall of a magnet as it slows down while passing through a conducting tube. We complement recent work by considering the effect of the thickness of the tube on the time of fall. The resulting expression gives a more accurate expression for the time of fall. [ABSTRACT FROM AUTHOR]