# Angular momentum / conservation of momentum questions

• qsduahuw
In summary: The integral is not well-defined because it is not clear what the limits of the region are. The integral is not well-defined because it is not clear what the limits of the region are.
qsduahuw
Homework Statement
See image below.
Relevant Equations
N/A
I thought the answer is B because the angular momentum in conserved in all 3 pictures.

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Delta2
qsduahuw said:
Homework Statement:: Answer to this question:

Relevant Equations:: N/A

I thought the answer is B because the angular momentum in conserved in all 3 pictures.

Conservation of angular momentum can only be assumed if no external torque operates. As the student manipulates the wheel, what external forces act on the student-wheel system? What torques might they exert?

Delta2
I am not an expert in angular momentum but something tells me that states B and C have same magnitude (and opposite direction ) of angular momentum so the correct answer must be one from (a) or (d)

Delta2 said:
I am not an expert in angular momentum but something tells me that states B and C have same magnitude (and opposite direction ) of angular momentum so the correct answer must be one from (a) or (d)
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.

haruspex 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.
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.

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.
I was careful only to say that it might not be conserved.

jbriggs444
haruspex said:
I was careful only to say that it might not be conserved.
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.

qsduahuw said:
I thought the answer is B because the angular momentum in conserved in all 3 pictures
Angular momentum is a vector. For it to be conserved, it must have the same magnitude and direction in all three pictures. Does it?

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.
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 and kuruman
jbriggs444 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?
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?

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?
What is the direction of a zero displacement?

haruspex said:
What is the direction of a zero displacement?
Sorry due to my chronical disease I haven't slept well and I got no clue what you try to imply.

Delta2 said:
Sorry due to my chronical disease I haven't slept well and I got no clue what you try to imply.
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.

Edit: Also note that the objection people are raising is that the direction of angular momentum may be undefined. Not that angular momentum itself is undefined.

Orodruin said:
Edit: Also note that the objection people are raising is that the direction of angular momentum may be undefined. Not that angular momentum itself is undefined.
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?

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?
Pay attention to the edit from @Orodruin in #13

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?
As I wrote, angular momentum is well defined. It is its direction that is not.

Orodruin said:
As I wrote, angular momentum is well defined. It is its direction that is not.
Ok let me ask you this, how can a vector be well defined, if its direction is not well defined?

Delta2 said:
Ok let me ask you this, how can a vector be well defined, if its direction is not well defined?
Let me ask you the same question. Which unique vector is this true for?

Delta2 said:
Ok let me ask you this, how can a vector be well defined, if its direction is not well defined?
Did you try to answer my question in post 11?

Orodruin said:
Let me ask you the same question. Which unique vector is this true for?
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.

haruspex said:
Did you try to answer my question in post 11?
I don't even understand your question. What a zero displacement has to do with this problem?

I feel a piece of information is very obvious to you guys but it's not obvious to me at all. I need to try to sleep, i ll come back in 2-3hours, hopefully with a clearer mind.

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.
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.

Oh ok i see the zero vector.

jbriggs444
Perhaps it would be helpful to ask what direction does the torque, if any, act relative to the angular momentum of the wheel? Can such a torque change the magnitude of the angular momentum of the spinning wheel? (assume there is no friction).

AM

## 1. What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of an object. It is a vector quantity, meaning it has both magnitude and direction, and is defined as the product of an object's moment of inertia and its angular velocity.

## 2. What is conservation of momentum?

Conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant over time, regardless of any internal or external forces acting on the system. This means that the total momentum before an interaction or event must be equal to the total momentum after.

## 3. How is angular momentum conserved?

Angular momentum is conserved in a closed system when there is no net external torque acting on the system. This means that the total angular momentum of the system remains constant, even if individual components may change their angular momentum.

## 4. What is the difference between linear momentum and angular momentum?

Linear momentum refers to the motion of an object in a straight line, while angular momentum refers to the rotational motion of an object around a fixed axis. Linear momentum is a product of an object's mass and velocity, while angular momentum is a product of an object's moment of inertia and angular velocity.

## 5. How is angular momentum related to rotational inertia?

Angular momentum and rotational inertia are directly related to each other. Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. The greater the rotational inertia, the greater the angular momentum needed to produce a given angular velocity.

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