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 ($I = \tfrac25 m r^2$).

• Rhett Allain, “Rolling Object Accelerating Down an Incline”, Wired, 29 Jul 2014, url https://www.wired.com/2014/07/a-rolling-object-accelerating-down-an-incline/ [20221129].