Rolling down on Incline

A rigid body with mass $m$ and radius $r$ will roll down on incline with linear acceleration $a$ along the incline

$$\tag{1} a = \frac{g \sin\theta}{1 + I / mr^2} $$

where $\theta$ is angle of the incline with horizontal direction and $I$ is moment of inertia of the rigid body. Previous equation becomes

$$\tag{2} a = \tfrac23 g \sin\theta $$

for a solid disk ($I = \tfrac12 m r^2$) and

$$\tag{3} a = \tfrac57 g \sin\theta $$

for a solid sphere ($I = \tfrac25 m r^2$).