A four-tensor momenta equation for rolling physics

Scientific theories, e.g. Newton’s second law, are always subject to revision. They are useful in guiding scientific research until an experiment proves them wrong and new knowledge is gained. Although provisional and premature when first proposed, scientific theories are necessary and must be stated at some point. The scientific approach benefits from the results obtained through these theories [1], and equations developed by earlier physicists should be updated as new knowledge is acquired [2]. In this sense, and according to J A Wheeler, the ultimate goal of physicists would be to express the laws of physics in the language of space and time [3].

In this work, we apply the advances of Einstein’s special theory of relativity [4] compared to classical physics to develop a four-tensor momenta equation to analyze rolling—linear translation with rotation (T&R)—processes [5].

With this four-tensor momenta equation formalism we will discuss rolling processes in mechanical energy conservation, mechanical energy dissipation by friction and mechanical energy production by a chemical reaction [6].