Final answer:
The student's question about the angular motion and tension in a mechanical system with two connected cylinders lacks complete information. The concepts of conservation of angular momentum, work-energy theorem, and net torque are typically employed to solve such problems in Physics.
Step-by-step explanation:
Understanding Angular Motion and Tension in a Mechanical System
This question falls under the category of Physics, specifically dealing with rotational motion, angular velocity, and tension. Unfortunately, the student's question lacks complete information to give a specific answer; it references diagrams and conditions that are not provided. However, we can discuss the concepts that are typically used to solve such problems. When considering the deceleration of cylinder B from 30 rad/s to 5 rad/s, we may use conservation of angular momentum if no external torques are acting on the system or employ the work-energy theorem if there's an applied force. For tension in the belt, we have to consider the net torque on either cylinder caused by the belt's tension and the respective angular accelerations of the cylinders.
To determine the distance cylinder A will rise, the difference in kinetic energies between the initial and final angular velocities can be equated to the work done by the weight of cylinder A moving upwards. In contrast, the tension in the belt can be calculated by analyzing the forces necessary to decelerate cylinder B and, if the system is assumed to be frictionless, accelerating cylinder A.