Final answer:
The global popularity of rap music is due to the mechanism of cultural change known as Diffusion, specifically hierarchical and stimulus diffusion.
Step-by-step explanation:
The mechanism of cultural change responsible for the global popularity of rap music is Diffusion. This refers to the spread of cultural elements from one society to another. As rap music originated in the United States, it followed a hierarchical diffusion pattern, moving from major cities like New York to other large and eventually smaller cities worldwide. Artists and DJs have played vital roles in this process through relocation diffusion, moving from one place to another and taking the culture with them. Adaptations to local customs and preferences are seen in stimulus diffusion, where core aspects of hip hop evolve to fit different cultural contexts.