An impulse to the ground to end rolling with slipping

TL;DR

This paper introduces a novel impulse-based method to analyze the transition from slipping to pure rolling in various scenarios, simplifying complex friction interactions through conservation laws.

Contribution

It presents a new technique using an unknown impulse to efficiently determine the final state of rolling with slipping scenarios without detailed friction calculations.

Findings

The method effectively predicts the final rolling state in different scenarios.

Conservation laws combined with impulse analysis simplify complex friction problems.

The approach provides a compact alternative to explicit friction calculations.

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.