The law of conservation of momentum is a fundamental law of nature. It states that the momentum of an isolated system is conserved. In high school or introductory-level physics courses, for simplicity, teachers and textbooks always use collisions in one dimension as the examples to introduce the concept of conservation of momentum. To solve simple…

Owing to the presence of the Coriolis effect, the rotation of Earth has a multitude of surprising consequences that make the mechanics of the atmosphere or the oceans different from that of a fluid in a container. Since the Coriolis effect also captures the imagination of screenwriters, contributing to the continual exposure of students to bogus…

In the same chapter of his book "Opera Geometrica," Torricelli published two discoveries: 1) initial velocity of a jet from a container increases with the square root of the depth of the hole; 2) he drew the pattern of jets from three openings at the wall of a container filled with water to constant level "H" and determined the…

A challenge: Can you create a stable top from a single paper clip? Several interesting solutions to this problem were provided by Takao Sakai from Japan, the requirement of each being that the center of gravity be located on the vertical y-axis at the center of the top. In the simplest configuration, we see that there exists a single angle ?…

Newton's cradle, a device consisting of a chain of steel balls suspended in alignment, has been used extensively in physics teaching to demonstrate the principles of conservation of momentum and kinetic energy in elastic collisions. The apparent simplicity of the device allows one to test commonly hold views regarding the intuitive understanding…

The Lorentz transformation applies directly to the kinematics of moving particles viewed as geometric points. Wave propagation, on the other hand, involves moving planes which are extended objects defined by simultaneity. By treating a plane wave as a geometric object moving at the phase velocity, novel results are obtained that illustrate the…

The objective of this introduction to Colombeau algebras of generalized functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic nonlinear problems in classical physics. Examples are given in hydrodynamics and electrodynamics. The problem of the…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…

At the pre-college and first-year college level of physics instruction, Kepler's laws are generally taught as empirical laws of nature. Introductory physics textbooks only derive Kepler's Second law of areas. It is possible to derive all of Kepler's laws mathematically from the conservation laws, employing only high-school algebra and geometry.…

We investigated the common difficulties that students have with concepts related to rotational and rolling motion covered in the introductory physics courses. We compared the performance of calculus- and algebra-based introductory physics students with physics juniors who had learned rotational and rolling motion concepts in an intermediate level…

Investigates the construction of understanding of the motion of an object down an inclined plane which takes place through the process of model building in an integrated algebra, trigonometry, and physics class. Discusses four major themes related to student learning through modeling that emerged from the results. Discusses implications for…