The discussion revolves around the conservation of angular momentum in a scenario involving a spinning wheel and a person on a rotating platform. Participants explore the conditions under which angular momentum can be considered conserved, particularly in relation to external torques and the direction of angular momentum in different states.
The discussion is ongoing, with participants raising questions about the definitions and implications of angular momentum and torque. Some guidance has been offered regarding the conditions for conservation and the nature of angular momentum as a vector, but no consensus has been reached.
Participants note the potential for external torques affecting the system and the ambiguity surrounding the direction of angular momentum in certain states. There is also mention of the need for clarity regarding the definitions being used in the discussion.
qsduahuw said:
I find the image in post #1 too blurry to be sure, but it looks to me that a, b and d all have B and C equal.Delta2 said:
Yes, right, but the OP implies that he has been told that (b) is not the correct answer and so does your post implies an external torque so AM is not conserved.haruspex said:
I was careful only to say that it might not be conserved.Delta2 said:
I agree it cannot be conserved. In state A I think angular momentum is in the horizontal direction , while in state b and C in the vertical direction.haruspex said:
Angular momentum is a vector. For it to be conserved, it must have the same magnitude and direction in all three pictures. Does it?qsduahuw said:
Be a bit careful with that claim about the direction of the angular momentum in (b) and (c). If it is defined at all, it is vertical. But is it defined at all?Delta2 said:
Sorry no clue why it is not defined?. We have some sort of double rotation: We have the wheel spinning and the person and wheel rotating around the platform center, kind of like Earth spinning around itself and rotating around the sun, why it should not be defined?jbriggs444 said:
What is the direction of a zero displacement?Delta2 said:
Sorry due to my chronical disease I haven't slept well and I got no clue what you try to imply.haruspex said:
Consider what kind of torques that could act on the system given that it is supported by a (presumably frictionless) support rotating freely around its axis and what this implies for the vertical component of the angular momentum.Delta2 said:
Sorry I still don't understand. If I take the following integral $$\int \vec{r}\times\vec{v} dm$$ over the whole region of our system (spinning wheel+person+rotating platform) isn't this integral well defined? Isn't it the angular momentum of the system?Orodruin said:
Pay attention to the edit from @Orodruin in #13Delta2 said:
As I wrote, angular momentum is well defined. It is its direction that is not.Delta2 said:
Ok let me ask you this, how can a vector be well defined, if its direction is not well defined?Orodruin said:
Let me ask you the same question. Which unique vector is this true for?Delta2 said:
Did you try to answer my question in post 11?Delta2 said:
It is true for all vectors I know of. A force is well defined if both direction and magnitude is well defined. Same for the velocity of a particle. Same from every other vector.Orodruin said:
I don't even understand your question. What a zero displacement has to do with this problem?haruspex said:
A vector is well defined if its direction and magnitude are both well defined. Yes, that is correct. However, the reverse implication does not hold. There is a condition under which a vector can be well defined without its direction being well defined.Delta2 said: