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so , do you mean the book is wrong? the moment ( so-called resultant force ) should be pointing downward if I use M=r x FOrodruin said: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.
No, the book is correct. Again, it is not a projection. And for the second time: a moment is not a resultant force.goldfish9776 said: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?
so , no matter M= r x F or M= F x r , the torque is in downward direction ?Orodruin said:No, the book is correct. Again, it is not a projection. And for the second time: a moment is not a resultant force.
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 said:so , no matter M= r x F or M= F x r , the torque is in downward direction ?
Orodruin said: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.
thanks , Orodruin . Everything is clear nowOrodruin said: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.
so the standard definiton of moment is M= r x F , not M= F x r ?Orodruin said: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.
Yes, because in general, r × F ≠ F × r, because the vector cross product does not commute.goldfish9776 said:so the standard definiton of moment is M= r x F , not M= F x r ?
SteamKing said:vector cross pr
Can you explain why is it r × F ? but not F × rSteamKing said:Yes, because in general, r × F ≠ F × r, because the vector cross product does not commute.
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.goldfish9776 said: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 said:Can you explain why is it r × F ? but not F × r
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 said: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.
then how about the right hand grip rule ? how to use it ?FactChecker said: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.
The Right Hand Thumb Rule is a method used to determine the direction of the resultant force when two or more forces act on an object. It is based on the fact that the direction of the resultant force is perpendicular to the plane formed by the two or more forces.
To use the Right Hand Thumb Rule, you need to align your hand with the plane formed by the two or more forces. Then, point your thumb in the direction of the first force, and your fingers in the direction of the second force. The direction in which your thumb points is the direction of the resultant force.
Yes, the Right Hand Thumb Rule can be used for any number of forces. Simply align your hand with the plane formed by the forces and follow the same steps as mentioned above.
If the forces are not in the same plane, the Right Hand Thumb Rule cannot be used. In this case, you will need to use a different method, such as the Parallelogram Law or the Triangle Law, to determine the resultant force.
The Right Hand Thumb Rule is a useful and accurate method for determining the direction of the resultant force in most cases. However, it may not be accurate if the forces are not coplanar or if they are not acting at a single point on an object.