Energy Inventory in the Sliding and Rolling Regimes

The energy inventory during the transition between the sliding and rolling regimes has frequently received short shrift in the physics and engineering literature. Here we delve into the intricacies of sliding and rolling motion and emphasize the salient points often missed in a cursory analysis which tends to focus mostly on torque and angular momentum. We show, for instance, that when a spinning cylinder slides and skids and ends up rolling, it loses two-thirds of its initial kinetic energy doing work against friction. Moreover, this number is independent of the coefficient of friction! This sounds counterintuitive at first blush. We help the reader develop an intuition for these counterintuitive rolling and sliding scenarios by a simple comparison that will remind the reader that they have seen this concept in a more familiar context before. When a car slams on the brakes and skids to a stop the loss of the initial kinetic energy to heat is not dependent on the coefficient of friction. If the coefficient of friction increases the stopping distance decreases and vice versa but the kinetic energy lost to heat remains the same. The more mysterious aspect in the rolling/sliding cylinder is the exact factor 2/3 regardless of the coefficient of friction. We have programmed an app with App Inventor to simulate various scenarios in order to help develop the intuition which we have found lacking in students of physics and engineering.