It looks like the standard equation of motion for a rigid body rolling without slipping down an incline of angle $\theta$ is
$$ a \;=\; \frac{g\sin\theta}{1 + I/(mR^2)}, $$
where $m$ is the mass, $R$ the radius, and $I$ the moment of inertia about the center of mass.
Recently I came across something called a snail ball (see image below): it’s a ball inside another ball, with a viscous filling such as molasses. The result is that it rolls much more slowly than a uniform sphere. (Action Lab also has a demonstration using a metal sphere inside a ball containing molasses: https://www.youtube.com/watch?v=ry-vQZD4E1U) A similar effect happens with a jar of molasses rolling when full vs. half full.
My question is: How does the rolling-without-slipping formula change for concentric shells or layered structures or by partial filling of each cavity or different densities?
