Sliding-cum-rotational motion along an inclined plane

This article discusses a scenario/arrangement whose statics/dynamics/kinematics can be understood using the ideas of classical mechanics.
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A rolling-capable object on an incline, cross sectional view. The object may be a cylinder or sphere, among other possibilities.

The scenario here is a dry body placed on a fixed dry inclined plane with an angle of inclination $\theta$ with the horizontal, where the body is capable of rolling along the flat incline. This includes the following possibilities for the body: solid cylinder, hollow cylinder, cylindrical annulus, solid sphere, hollow sphere.

The extremes are $\theta =0$ (whence, the plane is horizontal) and $\theta =\pi /2$ (whence, the plane is vertical).