Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 11 - Rolling, Torque, and Angular Momentum - Problems - Page 320: 4b

Answer

If a frictionless block were to slide down the incline at that angle, its acceleration magnitude would be more than $0.10~g$ An opposing force of static friction directed up the incline causes the magnitude of the acceleration of the sphere's center of mass to be less than the magnitude of the acceleration down a frictionless incline.

Work Step by Step

If a frictionless block were to slide down the incline at that angle, its acceleration magnitude would be more than $0.10~g$ Since the ball rolls down the incline instead of sliding, there must be a force of static friction directed up the incline that gives the sphere an angular acceleration. This opposing force of static friction causes the magnitude of the acceleration of the sphere's center of mass to be less than the magnitude of the acceleration down a frictionless incline.
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