Total momentum of a rotating object

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Discussion Overview

The discussion revolves around the concept of total momentum in the context of collisions involving rotating objects and their interaction with linearly moving objects. Participants explore the relationship between linear momentum and angular momentum, particularly in collision scenarios.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants express confusion about how linear and angular momentum interact during collisions, particularly when a rotating object collides with a linearly moving object.
  • It is noted that linear and angular momentum are separately conserved, with changes in both being equal and opposite during collisions.
  • One participant questions how rotational movement can be translated to unidirectional movement, especially when a rotating object nearly stops due to a collision.
  • Another participant clarifies that total angular momentum is conserved, not just angular momentum about the center of mass, and that a body in pure translation can still possess angular momentum about a point.
  • There is a discussion about how the collision of two rotating objects can affect their linear and angular momentum, with examples provided to illustrate these concepts.
  • Clarification is sought regarding the definition of total angular momentum, which includes both angular momentum due to rotation and that due to translation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the translation of rotational movement to unidirectional movement, and there remains uncertainty about the implications of total angular momentum in collision scenarios.

Contextual Notes

Some assumptions about the definitions of linear and angular momentum, as well as the conditions of the collisions, are not fully explored, leading to potential gaps in understanding.

Tominator
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Hi
I am a bit puzzled by a specific type of collisions and distribution of momentum. Well, I know that the change in momentum of two coliding objects is equal and opposite. But I am not certain how is it in a case of collision of a directly moving object and a rotating one. Is the sum of a liner momentum and angular momentum, total momentum of a rotating object?
Thanks for answers.
 
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Linear and angular momentum are separately conserved. So the change in linear momentum of the colliding objects is equal and opposite, and so is the change in their angular momentum.
 
Doc Al said:
Linear and angular momentum are separately conserved. So the change in linear momentum of the colliding objects is equal and opposite, and so is the change in their angular momentum.

Well, but there are colisions, where the rotating object almost stops rotating thanks to colision wih another. So how is rotational movement translated to unidirectional in such a case?
 
Tominator said:
Well, but there are colisions, where the rotating object almost stops rotating thanks to colision wih another. So how is rotational movement translated to unidirectional in such a case?
What's conserved is total angular momentum, not just angular momentum about a body's center of mass. A body in pure translation will still have angular momentum about some point.
 
Doc Al said:
What's conserved is total angular momentum, not just angular momentum about a body's center of mass. A body in pure translation will still have angular momentum about some point.

I must admitt I do not understand this very well. Are you saying that it is not possible to translate rotational movement to unidirectional and vice versa? Because for example if two balls rotating clockwise crash, their rotation can cause them to move even quicker than before the crash. In an empty space, their rotation would be slower and their unidirectional movement would be quicker. I do not understand what you mean by total angular momentum, can you explain that please?
 
Tominator said:
Are you saying that it is not possible to translate rotational movement to unidirectional and vice versa? Because for example if two balls rotating clockwise crash, their rotation can cause them to move even quicker than before the crash. In an empty space, their rotation would be slower and their unidirectional movement would be quicker.
However they move after the collision, their total linear momentum and total angular momentum will be the same.
I do not understand what you mean by total angular momentum, can you explain that please?
Sure. Total angular momentum = Angular momentum due to rotation about the center of mass + angular momentum due to the translation of the center of mass.

That second part may be new to you. Here's an example. Say a particle is moving with speed v in the +x direction at some distance d from the x-axis. What is its angular momentum about the origin? L = r X mv, so its angular momentum = mvd.

If this "particle" were really an object rotating about its center of mass, then you'd have to add the angular momentum due to that rotation to get the total.
 
Thanks for answers
 

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