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

[Paul P]

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

 

[Taftarat]

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..

 

[Paul P]

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?

 

[Taftarat]

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.

 

[PJC01]

I would like to clarify some concepts and provide a response to your questions.

Firstly, random motion and rotation are two different types of motion. Random motion refers to the unpredictable movement of particles due to their random velocities and collisions with each other. On the other hand, rotation refers to the circular movement of an object around an axis.

In the first scenario, where there is a central fixed axis, the particles will continue to move randomly and collide with each other, but the central object will not move due to its fixed axis. Therefore, after a long enough time, the angular displacement of the central object will be close to zero since it has not experienced any rotation.

In the second scenario, where the central object is replaced with a shaped object, the particles will still move randomly and collide with each other, but the shaped object will also experience rotational movement due to its shape. The direction of rotation will depend on the shape of the object and the direction of the collisions with the particles. Without more information about the shape and the initial conditions of the system, it is not possible to determine the exact angular displacement of the shaped object after a long enough time.

I hope this clarifies some concepts and answers your questions. If you have any further inquiries, please let me know.