# Moment of force

1. Sep 16, 2015

### goldfish9776

the moment is r X F = rFsin tetha
which means r is projected to F , am i right . If so , then the resultant force should point downwards( by using right hand thumb rule) , am i right?

#### Attached Files:

• ###### DSC_0068.JPG
File size:
54.9 KB
Views:
106
Last edited by a moderator: Sep 17, 2015
2. Sep 17, 2015

### Orodruin

Staff Emeritus
I think you are thinking right, but it is difficult to tell because you use the wrong nomenclature. First of all, a cross product is not a projection. Second, the result of that cross product is not a force, it is a torque (which is the common name for a force moment of this form). "Resultant" is normally used for the result of a vector sum, not for a cross product.

3. Sep 17, 2015

### goldfish9776

so , do you mean the book is wrong? the moment ( so-called resultant force ) should be pointing downward if I use M=r x F
If i use M= F X r , then the torque should be acting upwards?

Last edited: Sep 17, 2015
4. Sep 17, 2015

### Orodruin

Staff Emeritus
No, the book is correct. Again, it is not a projection. And for the second time: a moment is not a resultant force.

5. Sep 17, 2015

### goldfish9776

so , no matter M= r x F or M= F x r , the torque is in downward direction ?

6. Sep 17, 2015

### Orodruin

Staff Emeritus
No, you cannot go around changing the definitions arbitrarily. The cross product changes sign if you change the order and only one of the definitions is standard. In the example in the book, the torque should point up.

7. Sep 17, 2015

### goldfish9776

the book changes the order from the top to the bottom . the book give M= r x F at the upper part , then it changes to M= F ( r sin tetha ) at the bottom. Which is the standrad definition ?

8. Sep 17, 2015

### Orodruin

Staff Emeritus
It does not change order, the second equation is just the magnitude and all quantities in it are scalars. The order in a product of scalars is irrelevant.

9. Sep 17, 2015

### goldfish9776

thanks , Orodruin . Everything is clear now

10. Sep 17, 2015

### goldfish9776

so the standard definiton of moment is M= r x F , not M= F x r ?

11. Sep 17, 2015

### SteamKing

Staff Emeritus
Yes, because in general, r × F ≠ F × r, because the vector cross product does not commute.

12. Sep 17, 2015

### goldfish9776

Can you explain why is it r × F ? but not F × r

13. Sep 17, 2015

### Orodruin

Staff Emeritus
This is a definition, it is how torque is defined. You could have defined it the other way around, but you would then have to go back and rewrite all textbooks using the standard definition.

14. Sep 18, 2015

### FactChecker

In order to keep track of everything and keep signs straight, the "right had rule" is used. With the right hand, r x F makes r ~ the first finger, F ~ the second finger, and the torque is the thumb. If you mix up the sign convention, everything will get impossibly confusing.

15. Sep 18, 2015

### goldfish9776

what do u mean by r ~ the first finger, F ~ the second finger ? we have only finger point from r to the F , right ?

16. Sep 18, 2015

### FactChecker

To use the right-hand-rule on r x F, take your right hand and:
Hold your index finger, your middle finger, and your thumb all perpendicular to each other to form a coordinate system (index finger straight ahead, middle finger in at a right angle, thumb straight up)