**The Net Torque on a Cylinder**A one-piece cylinder is shaped as shown in the figure, with a core section protruding from the larger drum. The cylinder is free to rotate about the central z-axis shown in the drawing. A rope wrapped around the drum, which has radius \( R_1 \), exerts a force \( T_1 \) to the right on the cylinder. A rope wrapped around the core, which has radius \( R_2 \), exerts a force \( T_2 \) downward on the cylinder.**Diagram Explanation:**- The diagram shows a solid cylinder pivoted about the z-axis through the center.- Labeled components include: - \( R_1 \) and \( R_2 \) as the radii of the drum and core, respectively. - Forces \( T_1 \) and \( T_2 \) applied via ropes. - Points where forces are applied, with arrows indicating direction.**(a) What is the net torque acting on the cylinder about the rotation axis (which is the z-axis in the figure)?****SOLUTION***Conceptualize*: Imagine that the cylinder in the figure is a shaft in a machine. The force \( T_1 \) could be applied by a drive belt wrapped around the drum. The force \( T_2 \) could be applied by a friction brake at the surface of the core.*Categorize*: This example is a substitution problem in which we evaluate the net torque using the equation: \( \tau = rF \sin(\theta) = Fr \).(Use the following as necessary: \( T_1 \), \( T_2 \), \( R_1 \), and \( R_2 \).)The torque due to \( T_1 \) about the rotation axis is: \( \tau_1 = R_1 T_1 = \_\_\_ \). (The sign is negative because the torque tends to produce clockwise rotation.) The torque due to \( T_2 \) is: \( \tau_2 = R_2 T_2 = \_\_\_ \). (The sign is positive because the torque tends to produce counterclockwise rotation.)Evaluate the net torque about the rotation axis:\[\tau_{\text{net}} = \tau_2 - \tau_1 = R_2 T_2 - R_1 T_1 =

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Answered: The Net Torque on a Cylinder A…

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