Rolling without Slipping (Energy)

Static friction plays a crucial role in rolling without slipping: it provides the torque that causes rotation, yet it does no work. Understanding this apparent paradox is essential for applying energy conservation to rolling systems.

Why Static Friction Does No Work

Work done by a force is defined as $W = F \cdot d$, where $d$ is the displacement of the point where the force acts.

For rolling without slipping, the contact point is instantaneously at rest relative to the surface:

$$v_{\text{contact}} = v_\text{CM} - \omega R = 0$$

This condition defines "no slipping.

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