# Dynamic Confinement: Min Angular Velocity of Object for Solid Behaviour

• carmicheal99@ya
In summary, the conversation discusses the minimum angular velocity required for an object to behave solid to various objects. This involves a 2-dimensional geometry problem and the concept of conservation of angular momentum may be used to calculate the minimum velocity. However, a more detailed mathematical analysis is necessary to fully understand and solve the problem.
carmicheal99@ya
What is the minumum angular velocity of an object to behave solid to various objects?

I've tasked myself with determining the rotational velocity (omega) for (n) vertical beams rotating a distance (r) from common axis such that particles moving at a linear velocity (v) with a radius of (p) may not pass through the area generated by revolving the beams. To simplify things; thickness, length and mass of all objects have been neglected leaving that for later engineering challenges as such this is a 2 dimensional geometry problem now.

Another conceptual way to ask this would be: how fast must a fan spin so that a ball thrown at it will always bounce back? Or possibly how fast must a ring spin before you can touch it without losing a finger.

I started with the perimeter of the circle divided by the number of open sections made by placing the beams equidistant from one another then subtracting off the width of the beam and the diameter of the particle. This leaves the open space that must be traversed by the beams in time (t).

A little rearranging yields:
phi = ((2*pi*r)/n - r*theta - 2*p)/r
where:
phi = angle traversed by the beam to prevent passage of the particle

Solving the linear velocity for time to cross this gap and realizing that the time is the same for angular velocity to move the beam into position.

t = r/v = phi/omega

Work this out to obtain:
omega = -((theta*n - 2*pi)*r + 2*n*p)*v/(n*r*p)

Where:
theta = the angle covered by the width of the beam ----> width = r*phi
n = number of beams
pi = 3.14159...
r = radius of circle generated by revolving beams
v = linear velocity of particle

After analyzing this equation to see if it describes the behavior I want, it breaks down by yielding extremely fast velocities (tangential velocities >> c) for small particles. My question after all this background information is: What would be the next logical step in my studies to get around this particle model breakdown?

Last edited:
Is there a different approach?One possible approach is to use conservation of angular momentum. If the ball has some initial angular momentum, this can be used to calculate the minimum angular velocity required for the ball to not pass between the beams. A more detailed mathematical analysis of this approach is beyond the scope of this answer, but it is certainly a possible solution.

The minimum angular velocity required for an object to behave solidly to various objects will depend on a number of factors such as the size and shape of the object, the velocity and mass of the particles, and the number of beams used in the dynamic confinement setup. From the equation provided, it is clear that the angular velocity will increase as the number of beams and the linear velocity of the particles increase. However, the equation may not accurately describe the behavior for smaller particles due to the breakdown at high tangential velocities.

To overcome this issue, the next logical step would be to conduct experimental studies to observe the behavior of different objects and particles at varying angular velocities. This will provide more accurate data and can help identify any other factors that may affect the minimum angular velocity. Additionally, incorporating the thickness, length, and mass of the objects into the equation may also provide a more comprehensive understanding of the dynamic confinement system. Further research and experimentation will be necessary to fully determine the minimum angular velocity for solid behavior in this system.

## 1. What is dynamic confinement?

Dynamic confinement is a phenomenon in which an object is constrained or confined in a dynamic or moving environment. This can result in changes in the behavior or properties of the object.

## 2. How is dynamic confinement different from static confinement?

Static confinement refers to an object being confined in a stationary or non-moving environment. Dynamic confinement, on the other hand, involves an object being constrained in a dynamic or moving environment. This can lead to different effects on the behavior of the object.

## 3. What is the minimum angular velocity required for solid behavior in dynamic confinement?

The minimum angular velocity required for solid behavior in dynamic confinement varies depending on the specific system and conditions. In general, the higher the angular velocity, the more likely it is for the object to exhibit solid behavior. However, there is no specific threshold and it can also depend on factors such as the shape and size of the object.

## 4. How does dynamic confinement affect the properties of an object?

Dynamic confinement can have various effects on the properties of an object. It can change the object's shape, size, and mechanical properties such as stiffness and strength. It can also lead to changes in the object's behavior, such as increased friction or reduced mobility.

## 5. What are some real-world examples of dynamic confinement?

One example of dynamic confinement is the behavior of particles in a fluid flow, such as sediment particles in a river. Another example is the confinement of molecules in a cell membrane, which can affect their movement and interactions. Dynamic confinement is also relevant in fields such as material science, where the properties of materials can be altered by subjecting them to dynamic constraints.

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