This paper investigates the principles and potential of rotational catapult mechanisms, specifically the sling effect, as efficient converters of angular momentum into linear momentum for propulsion and projectile acceleration. Building on \textit{Anglemetric Theory}, a framework developed emphasizing fundamental rotational physics, this work demonstrates how continuous rotational acceleration enables higher impulse delivery and energy efficiency compared to linear methods. Through theoretical analysis and thought experiments, it illustrates momentum conservation via angular-linear transformations and the inherent advantages of rotational systems, including controlled acceleration, gyroscopic stabilization, scalability, silent operation, and energy regeneration. Practical considerations such as centripetal force constraints and recoil dynamics are discussed. The findings suggest that sling-based rotational propulsion offers a promising, scalable alternative for applications ranging from terrestrial launch systems to advanced aerospace propulsion.