(Solved): A spool of thread consists of a cylinder of radius \( R_{1} \) with end caps of radius \( R_{2} \) ...

A spool of thread consists of a cylinder of radius \( R_{1} \) with end caps of radius \( R_{2} \) as depicted in the end view shown in the figure below. The mass of the spool, including the thread, is \( \mathrm{m} \), and its moment of inertia about an axis through its center is 1 . The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force \( \overrightarrow{\mathrm{T}} \) 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 \[ f=\left(\frac{1+m R_{1} R_{2}}{1+m R_{2}^{2}}\right) T \text {. } \] (Submit a flie with a maximum size of 1 MB.) No file selected. This answer has not been graded yet. (b) Determine the direction of the force of friction. to the left to the right straight up straight down