5.2 Connecting Rotational to Linear Kinematics

Linear Motion in Rotational Motion

In rotational motion, objects rotate around an axis. While this can be described as a rotational motion, you can also see that any point along the object will also be moving linearly in a circle. The distance between the point and the axis of rotation is represented with the variable ${r}$.

By definition of the radian, the linear position (${\Delta s}$) that a point moves when it is rotated is equal its distance from the axis (${r}$) multiplied by the angular displacement (${\Delta \theta}$), which gets the equation: ${\Delta s=r \Delta \theta}$. From this derivation, we can derive many more relationships, such as ${s=r \theta}$, ${v=r \omega}$, and ${a=r \alpha}$.