# Homework Help: Distance between the force and origin

1. Sep 17, 2015

### goldfish9776

1. The problem statement, all variables and given/known data
In this note , I was told that either vector OD , OC , AD and AC can be used as the distance between the Force and OA axis ... why ? To produce moment , the distance r must be originate from the origin of force ( point C ) , am i right ? So , IMO, only r AC can be used...

2. Relevant equations

3. The attempt at a solution

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2. Sep 17, 2015

### Staff: Mentor

Note the presence of the cross product when calculating the moment. Would any of those choices give a different result?

3. Sep 17, 2015

### goldfish9776

Sorry, I still don't understand. Can you explain further?

4. Sep 17, 2015

### Staff: Mentor

Realize that when you take the cross product $\vec{r} \times \vec{F}$, where $\vec{r}$ is a vector starting at pt O and extending anywhere along the line of $\vec{F}$, that you get the same answer. Essentially you are finding the perpendicular distance between pt O and the line.

In simpler terms: r X F = r sinθ F. Realize that when r changes, θ also changes so that r sinθ remains the same. Play around with this until you get it.

5. Sep 17, 2015

### goldfish9776

from the figure , it show that the vector r _OD is not along the vector F ....
By saying $\vec{r}$ is a vector starting at pt O and extending anywhere along the line of $\vec{F}$ , do you mean like this ? the r can be any vector ( in different colours ) along the vector F ?

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6. Sep 17, 2015

### goldfish9776

Since Force at C is moved towards D , why not Vector r_CD is used ?

7. Sep 18, 2015

### Staff: Mentor

Yes.

8. Sep 18, 2015

### Staff: Mentor

Vector r begins at pt O.

9. Sep 18, 2015

### goldfish9776

sorry, I'm still confused now . IMO, vector r _OD is not along the vector F .

10. Sep 18, 2015

### goldfish9776

Can you explain further?

11. Sep 18, 2015

### Staff: Mentor

That's true, it is not. Why would you think it would be?

Are you confusing it with vector CD?

12. Sep 19, 2015

### goldfish9776

Becoz I was told that the vector r must originate from anywhere along line of action ( force)

13. Sep 19, 2015

### Staff: Mentor

The vector r originates at point O and terminates anywhere along the line of action of the force.

14. Sep 19, 2015

### goldfish9776

the line of action refers to the line along F , right ? Vector CD isn't on this line , so i think vector CD is not suitable ...

15. Sep 19, 2015

### Staff: Mentor

Right.

Looks to me like F points along the line CD.

16. Sep 19, 2015

### goldfish9776

Ya, it points along cd? Why vector cd is not used? But vector od is used?

17. Sep 19, 2015

### Staff: Mentor

You seem to be mixing up $\vec{r}$ with $\vec{F}$. The vector r must begin at O and end somewhere on the line of action of F. So r could be OD or OC or anything in between, but not CD!

18. Sep 19, 2015

### goldfish9776

oh , yeah . I forgot that F can be longer . It doesnt necessarily ends at point D. that's why I'm confused.

19. Oct 15, 2015

### goldfish9776

if i use MOA = uOA . (rOC X F) , then my ans = 108 , if i use MOA = uOA . (rOD X F) , then the ans = 100 , is it correct ?

20. Oct 16, 2015

### goldfish9776

sorry , i didnt mean to spam , can someone help me with this ?

21. Oct 16, 2015

### Staff: Mentor

That cannot be correct. The point is that rOC X F = rOD X F.

22. Oct 16, 2015

### goldfish9776

Which part of my working is wrong?

23. Oct 16, 2015

### Staff: Mentor

Show your work. What are rOC, rOD, and F?

24. Oct 16, 2015

### goldfish9776

OD=0.6i +0.8j

25. Oct 16, 2015