A uniform solid sphere of radius is moving to the right across a horizontal surface at
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A uniform solid sphere of radius 0.12m is moving to the right across a horizontal surface at 2.4ms−1. At the same instant a sensor measures its angular speed about its center to be 15rads−1, clockwise as viewed from the right. The surface is rough enough to prevent long-term slipping.
Answer the following.
(a) Determine whether, at that instant, the sphere is rolling without slipping or rolling with slipping. Show your reasoning clearly.
(b) If the sphere is slipping, calculate the angular speed it must have (magnitude and direction) in order to roll without slipping while maintaining its center-of-mass speed of 2.4ms−1.
(c) For the slipping case, state whether the frictional force acting on the sphere tends to increase or decrease the magnitude of its angular speed. Justify your answer in terms of the relative motion at the point of contact.