We illustrate the derivations of Jeans' criteria for the gravitational instabilities in a static homogeneous Newtonian system for pedagogical objectives. The critical Jeans density surface is presented in terms of dimensionless sound speeds and (characteristic) length scales. (Contains 1 figure.)

The dynamics of some common sports, such as race walking, running, cycling, jumping, and throwing, are presented. Rough estimates of the relevant physical quantities required for these individual sports are discussed. General mathematical formulas are derived which can be used for judging the performance of any athlete. (Author/KR)

Starting from the energy and degeneracy of the Landau levels of a free-electron gas in a magnetic field, the nonoscillatory term of the Landau diamagnetism is derived for T=O, using elementary algebra only. (Author/JN)

"TK!Solver" was designed as a personal computing tool to solve problems involving mathematical calculations and analysis. An in-depth review of this model building and problem-solving package is provided. System commands, applications (including data lists, plots/graphs, iterative problem-solving, present values), and other areas are…

Since many texts use an incorrect argument in obtaining the instantaneous velocity of a rotating body, a correct and concise derivation of this quantity for a rather general case is given. (Author/SK)

Provides a simplified, synoptic overview of the area of thermodynamics, enumerating and explaining the four basic laws, and introducing the mathematics involved in a stepwise fashion. Discusses such basic tools of thermodynamics as enthalpy, entropy, Helmholtz free energy, and Gibbs free energy, and their uses in problem solving. (JM)

Presents a motion problem that students in a college physics class are asked to solve and later asked to continue to analyze until they have stopped learning from the problem or the problem itself is finished. (MDH)

Discusses the loss of precision that normally results in solving equilibrium problems, particularly as presented through the use of quadratic formulas in most introductory college chemistry textbooks. Provides examples of demonstrations. (TW)

Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)

Considers several aspects of quantitative relationships involved in learning physics. Includes discussions of proportionality, various kinds of equality, and the need for generality. Argues that clear distinctions are necessary if the physics curriculum is to be examined with regard to pupil outcomes. (TW)

Describes an activity in which the students utilize the mathematics concepts of ratio, proportion, and data tabulation to examine the relationship between air pressure, temperature, and humidity. Students learn to approximate partial pressure by using humidity and temperature readings and by interpolating from the vapor pressure-temperature table.…

Problems ask students to calculate the pressure against a billboard in high winds and the velocity of water flowing from a reservoir through a cylindrical pipe. Problem solutions incorporate computer tools such as spreadsheets. (MDH)