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JD_PM
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Conservation of Energy and Angular Momentum in a Rotating Train-Disk System
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Homework Help Overview
The problem involves a train departing from the center of a rotating disk, analyzing the conservation of angular momentum and energy within the system. The discussion includes finding the final angular velocity of the disk, comparing total energy states at different positions of the train, and evaluating work done by friction during the train's movement.
Discussion Character
- Mixed
Approaches and Questions Raised
- Participants explore the conservation of angular momentum and its implications for angular velocity and kinetic energy as the train moves from the center to a distance R.
- Some participants question the validity of energy conservation assumptions and the application of the parallel axis theorem in the context of the train's moment of inertia.
- There are attempts to derive expressions for kinetic energy at different positions and to relate work done against friction to kinetic energy lost.
- Concerns are raised about the clarity and correctness of the reasoning regarding the energy states and the moment of inertia of the system.
Discussion Status
The discussion is ongoing, with participants providing insights and corrections to each other's reasoning. Some have offered guidance on deriving expressions for kinetic energy and relating them to work done, while others are still seeking clarity on specific calculations and assumptions.
Contextual Notes
Participants note that the problem constraints include the requirement to consider the system's energy changes due to friction and the need for careful treatment of the moment of inertia as the train moves. There is also a focus on ensuring that all components of the system are accounted for in the calculations.