Forces Introduced in Accelerated Frames

One of the basic axioms of the special theory of relativity is that the laws of physics are the same in all unaccelerated frames of reference. That axiom, along with the constancy of the speed of light, lead to the results of the previous two blog entries in this collection. In this entry, we will look at some accelerated frames, especially rotating frames, to see that Newton's second law must be modified to account for the acceleration of one frame with respect to another. This modification is the introduction of apparent (or so called "fictitious" forces) that are a direct result of the accelerating frame. In the paper, Forces Introduced in Accelerated Frames we look at the forces introduced in rotating frames.

A Relativistic Dynamics Primer

In early Physics classes the conservation of momentum and conservation of energy are fundmental laws used in all kinds of applications. Momentum is defined as the product of mass and velocity. But it turns out that momentum has to redefined when the velocities involved become relativistic. This new definition has consequences in the concepts that depend on it. This paper Relativistic Dynamics Primer summarizes the basic ideas of momentum and energy when relativistic speeds are in play. In particular, it explains why the formula for momentum used in classical mechanics must be altered to satisfy conservation under a Lorentz transformation and how this change in the definition of momentum leads to the concept of mass as energy in a new formulation of relativistic total energy. The concepts reduce to the familiar Newtonian ones when the velocity is not relativistic. It assumes the reader is familiar with the concepts in the previous blog entry - A Special Relativity Primer. A few examples are worked to apply the concepts discussed.

Special Relativity Primer

The consequences of Special Relativity follow from the assertion that the laws of physics are the same in all inertial frames. In particular, the speed of light is a limiting constant in all such frames. The consequences, deduced from this assertion, make up a body of results that have been repeatedly affirmed in practice since the early 20th century. I once tried to describe some of these consequences in a paper I wrote in a Philosophy of Science class. The professor gave me an A on the paper but asked, in the end, do these things really happen? This paper, Special Relativity Primer, explains the basic theory and provides exampes and worked exercises demonstrating the consequences.