A conveyor belt in a factory moves to the right at a constant speed of
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A conveyor belt in a factory moves to the right at a constant speed of 0.80ms−1. A uniform solid cylinder of radius 0.10m and mass 2.0kg is gently placed on the belt with its axis horizontal and oriented perpendicular to the belt’s motion. When the cylinder first touches the belt, its center of mass is momentarily at rest and it is not rotating. The coefficient of kinetic friction between the belt and the cylinder is μk=0.25, and the belt speed remains constant throughout.
(a) Immediately after contact, what is the direction of the frictional force exerted by the belt on the cylinder? Explain using the relative motion at the point of contact.
(b) Assuming the frictional force remains kinetic until pure rolling is achieved, calculate the magnitude of the center-of-mass acceleration of the cylinder during the slipping phase.
(c) Determine the angular speed of the cylinder at the instant it first rolls without slipping on the belt.