## anonymous 4 years ago How do I know when to use M=u*(r X F) or M= r X F to find the Momentum

1. anonymous

Is that u times (r cross F) or is X a variable?$M = u \cdot (r \times F) ~~ {\rm or}~~ M = u \cdot (r \cdot X \cdot F)$

2. anonymous

times

3. anonymous

r cross F

4. anonymous

u dot product ( r cross product F)

5. anonymous

Okay. Another question: What quantity is u? I want to make sure we are on the same page here. I have a feeling we are defining angular momentum here and not translation momentum.

6. anonymous

7. anonymous

u needs to be found

8. anonymous

I know how to do it because the book shows it using the cartesian values but my question is when a problem is given to find M , how do I know if I use M=u*(r X F) or just M = r X F

9. anonymous

I got it. You are looking to calculate the moment not momentum. I would always use$M = r \times F$I don't know what u represents. If I know what it is, I can advise you on how to use it.

10. anonymous

In the example you have given, to find the moment about point A, using the following expression. $M_A = [0.6 \hat i + 0.3 \hat k] \times [-300 \hat k] = (0.6 \cdot -300) \cdot [\hat i \times \hat k] + (0.3 \cdot -300) \cdot [\hat k \times \hat k] = (0.6 \cdot 300) \hat j$

11. anonymous

$M_A = (0.6 \cdot 300) \hat j$

12. anonymous

u is the vector AB

13. anonymous

beccause the problem says find the Mab produced by the Force

14. anonymous

To find the moment about point B, $M_B = [0.2 \hat i - 0.2 \hat j + 0.3 \hat k] \times -300 \hat k$

15. anonymous

For a moment about the line through A and B, $M_{AB} = \vec u_{A/B} \cdot (\vec r_o \times F_C)$where $$\vec r_o$$ is the vector from any point of the segment AB to C.

16. anonymous

We use the vector $$\vec u_{A/B}$$ when we are finding the moment about a line or axis. We use the regular cross product when we are finding the moment about a point.

17. anonymous

$M_{line} = \vec u \cdot (r_o \times F)$$M_{point} = r \times F$

18. anonymous

Perfect!!!!! Thank you soooooo much!!! Couldn't be explained better!!!!