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 ?