An impulse to the ground to end rolling with slipping

Abstract: Several scenarios used in teaching feature a rolling motion with slipping that transitions to one without through friction with the ground. We summarise these transitions by introducing an unknown impulse that is transferred to the ground. Accounting for this in the conservation of angular and linear momentum, we can deduce the final state of these scenarios in a compact manner and without requiring details of the friction. Contrasting this technique with an explicit calculation of the friction illustrates how collisions and conservation laws allow to solve problems involving complex interactions by summarising them. We exemplify our technique with three scenarios: a moving ball starting to roll, a turning wheel being released on the ground, and a monowheel breaking.