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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SUMMARY

The discussion focuses on calculating the frequency of circular motion for a small ring of radius r rolling inside a cone with friction. The key conclusion is that the frequency ω is determined by the equation ω = (1/tan(θ)) * sqrt(g/(2h)), where g is the acceleration due to gravity and h is the height above the cone's tip. The participants clarify the role of torque and angular momentum in the precession of the ring, emphasizing that the torque due to friction along the slant height is essential for maintaining circular motion.

PREREQUISITES

Understanding of circular motion dynamics
Familiarity with torque and angular momentum concepts
Knowledge of frictional forces in rotational systems
Basic principles of gyroscopic motion

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Study the relationship between torque and angular momentum in rotating systems
Explore the dynamics of gyroscopic precession in detail
Learn about frictional forces and their effects on rolling motion
Investigate the mathematical modeling of motion in conical surfaces

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Physics students, mechanical engineers, and anyone interested in the dynamics of rotational motion and gyroscopic systems.

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!