Rolling without slipping is the most tested topic in rotational mechanics. The constraint v_cm = Romega connects translational and rotational motion. The contact point has zero velocity (instantaneous axis of rotation), and the topmost point has velocity 2v_cm.

On an incline, the acceleration a = g*sin(theta)/(1 + k^2/R^2) depends only on the shape (via k^2/R^2), not on mass or radius. Solid spheres (2/5) are fastest, followed by discs/cylinders (1/2), hollow spheres (2/3), and rings (1).

Static friction enables rolling but does zero work (contact point has zero velocity). It provides the torque for angular acceleration. The minimum friction coefficient for rolling without slipping on an incline: mu >= (k^2/R^2)*tan(theta)/(1 + k^2/R^2).

Energy conservation is the preferred method: Mgh = (1/2)Mv^2(1 + k^2/R^2).