Using Right Hand Thumb Rule to Determine Resultant Force

[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?

 

[Orodruin]

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.

 

[goldfish9776]

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.

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?

 

[Orodruin]

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?

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

 

[goldfish9776]

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

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

 

[Orodruin]

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

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.

 

[goldfish9776]

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.

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 ?

 

[Orodruin]

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.

 

[goldfish9776]

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.

thanks , Orodruin . Everything is clear now

 

[goldfish9776]

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.

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

 

[SteamKing]

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

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

 

[goldfish9776]

vector cross pr

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

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

 

[Orodruin]

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

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.

 

[FactChecker]

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

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.

 

[goldfish9776]

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.

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

 

[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)

With your fingers held that way, twist your hand so that:
Point the index finger in the direction of r.
Point the middle finger in the direction of the rejection of F on r. (The rejection of F on r is the component of F that is perpendicular to r.)

Your thumb will then point in the direction of the torque vector.

 

[goldfish9776]

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)

With your fingers held that way, twist your hand so that:
Point the index finger in the direction of r.
Point the middle finger in the direction of the rejection of F on r. (The rejection of F on r is the component of F that is perpendicular to r.)

Your thumb will then point in the direction of the torque vector.

then how about the right hand grip rule ? how to use it ?