A spool consists of a cylinder of radius R 1 wraped with thread and its end caps have radius R 2 as shown in the end view illustrated in figure. The mass of the spool, including the thread, is m,

Question

A spool consists of a cylinder of radius $R_{1}$ wraped with thread and its end caps have radius $R_{2}$ as shown in the end view illustrated 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 $T$ acting to the right is applied to the free end of the thread. Friction force exerted by the surface on the spool is given by :

CT46 m2 diagram

TestHub · Accepted Answer

Use ma=T+f and Iα=TR1-fR2 with a=αR2. This gives f=(I-mR1R2)T/(I+mR2²), directed right.

Physics - Rotation Question with Solution | TestHub

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