Rolling Motion

Definition

Rotation plus translation at once — a rolling wheel's bottom point is instantaneously at rest while the top moves twice as fast as the center.

Technical definition

For rolling without slipping, v_cm = ωR and the contact point has zero instantaneous velocity. Kinetic energy splits into ½mv² + ½Iω².

Example

A car moving at 20 m/s has wheels whose tops move at 40 m/s relative to the ground while the contact patch is momentarily still — which is why tires grip instead of skid.

Common confusion

Rolling without slipping is not sliding. If the contact point were moving, kinetic friction would act; the instant rest of the contact point is what lets static friction hold.