6.5 Rolling

Rolling Without Slipping

When an object rolls without slipping, its point of contact with the surface has zero velocity relative to the ground. This occurs because static friction ensures that the rotational and translational motions are synchronized.

At any instant:

The top of the wheel moves forward at speed ${v_{top} = 2v_{cm}}$

The center of mass moves at ${v_{cm}}$

The bottom point (in contact with the ground) is momentarily stationary (${v = 0}$)

Because there is no relative motion at the contact point, static friction does no work, meaning total mechanical energy is conserved.