How Does Particle Collision Influence Angular Displacement in a Closed System?

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Discussion Overview

The discussion revolves around the influence of particle collisions on the angular displacement of a central object in a closed two-dimensional system. Participants explore scenarios involving different shapes of the central object and the implications of particle movement on its rotation over time.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant questions the angular displacement of a central object in a closed system after a sufficient time T, suggesting it may be close to zero.
  • Another participant proposes that when the central object is replaced with a differently shaped object, it may prefer to rotate counterclockwise, though this is uncertain.
  • There is a discussion about the randomness of particle movement, with one participant suggesting that if particles move randomly, the central object's rotation depends on the number of impacts from particles.
  • Another participant counters that particles do not move truly randomly but deterministically, raising the question of whether collisions can still be viewed as random.
  • Participants discuss the symmetry of the first central object, suggesting that the probabilities of clockwise and counterclockwise rotation may be equal due to symmetry, while noting that the second object lacks such symmetry.
  • There is speculation about how the shape of the second object might influence the probabilities of its rotation, indicating a dependence on the object's geometry.
  • One participant emphasizes that the outcome may depend on the initial speeds and directions of the particles, suggesting that simulations could provide further insights.

Areas of Agreement / Disagreement

Participants express differing views on the nature of particle movement and its implications for the central object's rotation. There is no consensus on the angular displacement or the probabilities of rotation for the differently shaped objects, indicating multiple competing perspectives.

Contextual Notes

The discussion highlights uncertainties regarding the assumptions of particle movement and the influence of object shape on rotation probabilities. The mathematical modeling of these scenarios remains unresolved.

Paul P
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hi,
i have some question and i hope someone know answers:

Lets have closed two dimensional space with some particles, which have random position and random velocities. In the center of space is object, which has central fixed axis. This object has no velocity and no angular velocity. (see left side of attached image) That is starting state of system. After some time T, during which particles and object flexible bounces and central object make only rotational movement, system ends in some state.

my question is 1.) When time T is long enough, what is angular displacement of central object during time T ?
// i think close to zero ?

Lets change situation little bit. Take away central object and replace with another shaped object - see right side of attached image.

question is same 2.) When time T is long enough, what is angular displacement of shaped central object during time T ?
// i think, that shaped object will prefer rotate counterclockwise ... or not ?

thanks for answers
 

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Paul P said:
hi,
i have some question and i hope someone know answers:

Lets have closed two dimensional space with some particles, which have random position and random velocities. In the center of space is object, which has central fixed axis. This object has no velocity and no angular velocity. (see left side of attached image) That is starting state of system. After some time T, during which particles and object flexible bounces and central object make only rotational movement, system ends in some state.

my question is 1.) When time T is long enough, what is angular displacement of central object during time T ?
// i think close to zero ?

Lets change situation little bit. Take away central object and replace with another shaped object - see right side of attached image.

question is same 2.) When time T is long enough, what is angular displacement of shaped central object during time T ?
// i think, that shaped object will prefer rotate counterclockwise ... or not ?

thanks for answers

this is more math statistics then physics. if particles move randomly = center object moves randomly. its rotation depends on how many hits it received from one or other side..
 
Taftarat said:
this is more math statistics then physics. if particles move randomly = center object moves randomly. its rotation depends on how many hits it received from one or other side..

yes, i thought about it similar way, but particles don't move truly random, but deterministically.
In this case it is possible to look at it that particles collisions with central object is random?

From this perspective, probabilities of rotation clockwise and counterclockwise of first central object is equal - because of symmetries?

For second object, there is no such symmetry.
So what are these probabilities of rotation for second object?
Depends it on the shape of object?
 
Paul P said:
yes, i thought about it similar way, but particles don't move truly random, but deterministically.
In this case it is possible to look at it that particles collisions with central object is random?

From this perspective, probabilities of rotation clockwise and counterclockwise of first central object is equal - because of symmetries?

For second object, there is no such symmetry.
So what are these probabilities of rotation for second object?
Depends it on the shape of object?

i still think that it all depends on particle starting speed and direction. simulation would give more answers.
 

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