The equation GMm/R^2 = v^2/R is applicable in scenarios where circular motion is influenced by gravitational forces, such as in satellite or planetary motion. The right side of the equation represents centripetal force, which counteracts inertia and prevents linear motion. It is important to include mass on the right side to accurately represent acceleration as a force. The discussion emphasizes the context in which this equation holds true. Understanding these principles is crucial for analyzing gravitational fields and centripetal motion effectively.