Sliding and Rolling Motion

Wheels are common examples of systems undergoing general plane motion with both translation and rotation.

The wheel shown below can have 1 of 3 possible motion types:

1. Pure rolling motion. This occurs when there is no slip between the wheel and the surface. IN this case, $v=R\omega$.
2. Pure sliding motion. This occurs when the wheel is prevented from rotating (such as when a brake is applied). In this case, $\omega =0$ and $v\ne R\omega$.
3. Sliding and rolling motion. In this case $\omega \ne 0$. Because slipping occurs in this case, $v\ne R\omega$.

The wheel will roll without slipping (pure rolling) if the tangential force $f_t$ is smaller than the static friction force ${\mu }_{s}N$, where $N$ is the force of the wheel normal to the surface. In this case, the tangential force does no work because it does not act through a distance. If the static friction force is smaller than $f_t$, the wheel will slip.