Frequency of Circular Motion in Ring Rolling Inside a Cone

Thread starter Saitama
Start date Apr 3, 2014
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Cone Ring Rolling

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Homework Help Overview

The problem involves analyzing the frequency of circular motion of a small ring rolling inside a cone under the influence of friction. The setup specifies that the ring rolls without slipping and maintains a perpendicular orientation to the line connecting the point of contact to the tip of the cone.

Discussion Character

Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

Participants discuss the forces acting on the ring, particularly the role of friction and torque in maintaining circular motion. There is confusion regarding the effects of friction along the slant height of the cone and its contribution to torque.

Discussion Status

Participants are actively questioning and clarifying the mechanics involved, particularly the relationship between torque, angular momentum, and the forces acting on the ring. Some have provided insights into the nature of gyroscopic precession and the necessary conditions for the ring's motion, while others express uncertainty about specific calculations and assumptions.

Contextual Notes

There are ongoing discussions about the assumptions made regarding the forces and torques, particularly the absence of tangential friction and the implications for the motion of the ring. Participants are also exploring the relationship between angular velocities and the constraints of the problem.

Apr 24, 2014

Saitama

haruspex said:

The "point of contact" of one object on another does not refer to a fixed piece of the first object; it refers dynamically to that part of the first object which is contact with the second at any given instant. When a wheel rolls along a road, the point of contact is always on the road directly under the centre of the wheel. Thus, it moves along at the same speed as the wheel.
If the blue part you have marked is intended as a mark on the wheel, that will descriibe a cycloid. When it makes contact with the road (becoming, transiently, the point of contact) it is instantaneaously at rest.
The equation you wrote taking the velocity of the centre of the ring, then adding to that the relative velocity of a point on the ring, gave you the velocity of that piece of the ring which was instantaneously in contact with the cone. That velocity was therefore zero.

Ok, I see it now, thanks haruspex for your patience!