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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.

We describe an efficient method for determining the radii of spheres attached to atomic force microscope (AFM) cantilevers by minimizing the square root of the square error for a segment of circular arc cross-sectional data. The approach we present has benefits: (1) The method fits a function, with two fitting parameters, to a number of data points, rather than calculating the radius based on two points of cross-sectional data, (2) a fit is performed in a common spreadsheet application, using a solving feature, and (3) spheres of diameters 2 to 60 μm were measured to an accuracy of 9% and a precision of 4%. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Electrification by rubbing different materials is a well-known phenomenon with a history that began more than five centuries B.C. ago. However, simple experiments can lead to contradictory or inconsistent results, and the history of this phenomena is plagued with non-intuitive results. For example, triboelectric charging by rubbing identical materials is possible. In this work we want to highlight some historical aspects of triboelectricity that could enrich the discussion of electrostatics in an undergraduate physics course. We will focus on the effect of strain on the triboelectric properties of a sample, which we think is not well known to physics teachers. We will show that it is possible to obtain robust polarities by rubbing identical rubber balloons of different radii and we will also show that this charging method can be very useful in introductory physics courses. [ABSTRACT FROM AUTHOR]

The kinematics of a sphere of radius R and mass m bouncing elastically in a horizontal channel is studied in detail. Explicit expressions for the position and linear and angular velocities of the sphere at any collision are obtained. It is shown that if the moment of inertia 1= γmR2 is such that (1- γ)/(1 + γ)=cos 2π/k with k an integer and k⩾4, the motion is periodic, with repetition after k collisions for k even, and after 2k collisions for k odd. The motion of a homogeneous sphere (which is not periodic) is analyzed by investigating the mean properties of its velocities and positions. The analogy between this motion and that of a periodic oscillator is discussed. [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]

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]

A method to calculate growth stress in SiO2 scales formed during SiC fiber oxidation was developed. Calculations were done for Hi-NicalonTM-S SiC fibers using previously measured Deal-Grove oxidation kinetics parameters. Initial compressive stresses in SiO2 of ∼25 GPa from the 2.2× oxidation volume expansion are rapidly relaxed to lower levels by flow of silica with a shear-stress dependent viscosity. At >1200°, viscous flow of silica relaxes stress to negligible levels. At 700° - 900 °C, compressive axial and hoop stress at the GPa level persist, but radial stresses are much smaller. The decrease in growth stress with increase in temperature is a consequence of larger activation energy for silica viscosity than for oxidation kinetics. Radial expansion of the outer scale eventually causes hoop stress to become tensile in the outer scale, and axial stress becomes tensile from the Poisson effect. Tensile hoop stresses can be >1 GPa for thick scales formed at <1000 °C. Approximate analytical expressions for growth stress for some limiting cases are discussed. Growth stresses were also calculated for crystallized SiO2 scales; these were qualitatively consistent with microstructural evidence of stress. Assumptions and limitations of the calculation method are discussed, along with the possible effects of growth stress on SiC oxidation kinetics and on SiC fiber strength. [ABSTRACT FROM AUTHOR]