Unfurling a rolled-up sheet from a dispenser at constant speed

Abstract

Abstract An introductory physics problem asks for the applied force necessary to pull a strip of paper towels off a mounted roll at a constant tangential speed. Numerous online help sites provide inadequate solutions. Newton’s second law for rotations can be applied as the radius and hence the moment of inertia decreases. Several rolls of flexible materials having different dimensions and masses are characterized to show that the required force can increase, remain constant, or decrease as time elapses for a roll that rotates frictionlessly about a fixed axle.