A spool of thread consists of a cylinder of radius R1 with end caps of radius R2 as depicted in the end view shown in Figure. The mass of the spool, including the thread, is m, and its moment of inertia about an axis through its center is I. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force ? acting to the right is applied to the free end of the thread. (a) Show that the magnitude of the friction force exerted by the surface on the spool is given by ? = [(I + mR1R2)/(I +mR2^2)]T (b) Determine the direction of the force of friction.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A spool of thread consists of a cylinder of radius R1 with end caps of radius R2 as depicted in the end view shown in Figure. The mass of the spool, including the thread, is m, and its moment of inertia about an axis through its center is I. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force ? acting to the right is applied to the free end of the thread. (a) Show that the magnitude of the friction force exerted by the surface on the spool is given by

? = [(I + mR1R2)/(I +mR2^2)]T

(b) Determine the direction of the force of friction.

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