# Homework Help: What is the direction of the red ball's angular momentum

1. Apr 12, 2015

### Westin

1. The problem statement, all variables and given/known data

What is the direction of the red ball's angular momentum about the point A?
(see figure)

Same as the momentum.
Out of the page.
Zero magnitude.
Opposite to the momentum.
Same as rA.
Into the page.

2. Relevant equations
Angular Momentum

3. The attempt at a solution

I believe the answer is same as the momentum because the angular momentum is 'the moment of momentum'

#### Attached Files:

• ###### Screen Shot 2015-04-12 at 2.25.48 PM.png
File size:
56 KB
Views:
274
2. Apr 12, 2015

### rcgldr

Is the ball rolling up the plane or down the plane? If this is during an instant where the ball is stopped, then it has zero momentum.

3. Apr 12, 2015

### Westin

Unfortunately that info is not given, but if we assumed it was down wouldn't the answer just be same as momentum?

4. Apr 12, 2015

### Staff: Mentor

How do you determine angular momentum of a point-mass?

5. Apr 12, 2015

### SammyS

Staff Emeritus
The figure helps tremendously.

It looks to me like the ball is at the position of the red dot and is moving horizontally.

How do one calculate angular momentum ?

6. Apr 12, 2015

### Westin

L = r x p
L = same as momentum then ?

Last edited: Apr 12, 2015
7. Apr 12, 2015

### Staff: Mentor

r x p and p are not the same, and do not point in the same direction.
What do you know about the cross-product?

8. Apr 12, 2015

### Westin

Cross product is r⃗A × F⃗

This helps you find torque

9. Apr 12, 2015

### Staff: Mentor

10. Apr 12, 2015

### Westin

Opposite to the momentum?

11. Apr 12, 2015

### haruspex

If you have two vectors and take their cross product, $\vec c = \vec a \times \vec b$, what is the angle between $\vec a$ and $\vec c$? It is always the same answer.

12. Apr 12, 2015

### Westin

it is 180 degrees, I'm still a little lost of what the answer could be though..

13. Apr 12, 2015

### Staff: Mentor

It is not 180 degrees. Check the definition and basic properties of the cross-product.

14. Apr 12, 2015

### SammyS

Staff Emeritus
Do you know the Right Hand Rule for cross-product ?

15. Apr 12, 2015

### Westin

Vector C will be perpendicular to both A & B. The angle will be between 0 and 180 degrees

• A x B = A B sin([PLAIN]https://www.physics.uoguelph.ca/tutorials/torque/theta.gif) [Broken]

not familiar with right hand rule but I'm trying to learn it right now

Last edited by a moderator: May 7, 2017
16. Apr 12, 2015

### Staff: Mentor

Right.
You can know the exact angle between a and c. This is not the angle between a and b!

17. Apr 12, 2015

### Westin

It would be going out of the page then!?!?!?

because it will be pointing upwards

Last edited: Apr 12, 2015
18. Apr 12, 2015

### Staff: Mentor

Right.

19. Apr 12, 2015

### rcgldr

If the ball is rolling down hill (left to right), then the angular momentum vector points into the page (right hand rule).

20. Apr 12, 2015

### Westin

So who is right here? I only have one try

21. Apr 12, 2015

### SammyS

Staff Emeritus
@ rcgldr,
Look at the figure.

There is no downhill. The momentum of the ball is to the right, so the ball is moving to the right (horizontally). The ball is at a position below and to the right of point A.

There is no indication that the ball itself is rotating at all.

22. Apr 12, 2015

### SammyS

Staff Emeritus
That all depends upon who is interpreting the problem as it was intended.

Looking at the figure it appears that you may have previously tried the "Into the page " answer.

23. Apr 12, 2015

### Westin

The answer was out of the page, thanks everyone.

24. Apr 13, 2015

### haruspex

I see nothing in the statement about the ball's rotating, nor any indication of a vertical direction. It is shown as moving directly left to right, not at an angle to the page edge, so I don't think it can be intended as 'rolling downhill'.

25. Apr 13, 2015

### rcgldr

So is this a 3d image mapped into a 2d image and the vector labeled as "rA" is either pointed out from the page or into the page? The momentum vector is to the right, so maybe we assume the ball is rolling clockwise (rolling to the right), in which case the angular momentum vector should be into the page (right hand rule).

Last edited: Apr 13, 2015