The phrase "revolving on" has several synonyms that can be used depending on the context of the sentence. Some possible options include "hinging on," "centring on," or "focused on." Each of these phrases conveys the idea that something is at the core or center of a situation or issue and is pivotal to understanding it. Other potential synonyms for "revolving on" could include "turning around," "circling back to," or "relying on." These phrases emphasize the cyclical nature of a problem or situation and suggest that it may require ongoing attention or resolution. Regardless of the synonym chosen, each one offers a unique way of expressing the idea of something being central to a situation or decision.