How Can I Calculate the Angular Speed of a Ring Rolling Without Slipping?

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Homework Help Overview

The discussion revolves around calculating the angular speed of a ring rolling without slipping, specifically focusing on the relationship between the ring's motion and the geometry of its interaction with a smaller circle. The problem involves concepts from rotational dynamics and geometry.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the angular speed of the ring and the angular speed of a finger rotating it. There are attempts to clarify how the angles involved relate to the motion of the ring and the geometry of the setup. Questions arise regarding the interpretation of terms like "angle of orientation" and the concept of instantaneous axes of rotation.

Discussion Status

The discussion is ongoing, with participants providing insights and clarifications on the geometric relationships involved. Some participants have offered guidance on how to visualize the problem, while others express confusion about specific terms and concepts. There is no explicit consensus on the interpretation of the instantaneous axis of rotation.

Contextual Notes

Participants are navigating through complex geometric relationships and assumptions about motion without slipping. There are references to specific angles and their implications for the problem, but some details remain unclear, leading to further questioning and exploration.

  • #31
zwierz said:
It seems that it is supposed that the ring remains in a horizontal plane. Strange
Yes, strange. I don't see how it could move in a truly horizontal plane.
 
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  • #32
it would be a good task to write honest equations of stationary motion that is when an angle of ring's incline is constant and the speed of ring's center is constant and ring's center moves along a horizontal cirle
 

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