Abstract: This paper reviews the derivation methods of the mass-energy equivalence and momentum relations from the original literature, which are logically rigorous but procedurally complex, limiting their application in modern textbooks. The authors propose a novel derivation scheme based on the concept of “redistribution of kinetic energy and momentum”. By introducing the photon concept and incorporating the Doppler effect, the transformation relationships of energy and momentum in different inertial frames during symmetric photon radiation are analyzed. This approach simultaneously derives the mass-energy equivalence and relativistic momentum relations without relying on electrodynamics. The method is logically clear and mathematically concise, making it suitable for courses with limited teaching hours. It helps students understand the intrinsic connection between mass, energy, and momentum, offering new insights for improving the teaching of related content.

Key words: Lorentz transformation, mass-energy equivalence, relativistic momentum, kinetic energy, redistribution of kinetic energy and momentum