Reaction on the particle in terms of angular velocity

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Homework Help Overview

The problem involves a particle attached to a string moving in a circular path on a horizontal table, with the goal of finding the reaction force on the particle in terms of its angular velocity, ω. The setup includes considerations of forces acting on the particle, including gravitational and tension forces, as well as the geometry of the situation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the forces acting on the particle, including the normal force and the components of tension. There is exploration of how to express the reaction force in terms of angular velocity and the conditions under which the particle might lift off the table.

Discussion Status

Participants are actively engaging with the problem, questioning the meaning of "reaction" in this context and exploring the implications of their equations. Some have provided diagrams to clarify their understanding, while others are attempting to derive expressions for the forces involved. There is a recognition of the need to distinguish between different forces and their components.

Contextual Notes

There is some uncertainty regarding the definitions and roles of the forces involved, particularly the normal force and how it relates to the tension in the string. Participants are also considering the implications of the particle's motion and the conditions for it to remain on the table.

  • #31
Almost there. You need to solve for N not ω, that is have N by itself on the left side of the equation.
 
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  • #32
kuruman said:
Almost there. You need to solve for N not ω, that is have N by itself on the left side of the equation.
Hm, it indeed gets to N = m (g - 0.4 ω2). And that is the reaction on the particle in terms of ω?
 
  • #33
Yes it is. IMO it would have been clearer to have asked for the normal force in terms of ω.
 
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