Moment of force is considered concerning a point and concerning an axis. In the first case the moment of force is the vector having a certain direction. In the second case it is necessary to speak only about a vector projection to an axis.
Instruction
1. Let Q be a point concerning which moment of force is considered. This point is called a pole. Carry out r radius vector from this point to a point of application of force of F. Then the moment of force of M is defined as vector work r on F: M=[rF].
2. The vector is result of the vector work. Length of a vector is expressed by the module: | M |= |r| · |F| · sinφ, where φ – a corner between vectors of r and F. Vector of M ortogonalen to both r vector, and F vector: M⊥r, M⊥F.
3. The vector of M is directed in such a way that the three of vectors of r, F, M is right. How to define that the three of vectors right? Imagine as if you (your eye) are on the end of the third vector and you look at two other vectors. If the shortest transition from the first vector to the second seems the events counterclockwise, so it is the right three of vectors. Otherwise, you deal with the left three.
4. So, combine the beginnings of vectors of r and F. It can be done parallel translation of a vector of F in Q point. Now through the same point carry out the axis perpendicular to the plane of vectors of r and F. This axis will be perpendicular to both vectors at once. Here are possible to direct, in principle, only two options moment of force: up or down.
5. Try to direct the moment of force of F up, draw a vector arrow on an axis. From this arrow kind of look on a vector of r and F (you can draw a symbolical eye). You can designate the shortest transition from r to F by the rounded-off arrow. Whether the three of vectors of r, F, M is right? The arrow specifies the direction counterclockwise? If yes, that you chose a right direction for the moment of force of F. If is not present, so it is necessary to replace the direction with opposite.
6. It is possible to determine the direction of moment of force also by the rule of the right hand. Combine a forefinger about radius vector. Combine a middle finger with force vector. Since the end of the thumb raised up look at two vectors. If transition from index to a middle finger is carried out counterclockwise, then the direction of moment of force coincides with the direction which specifies a thumb. If transition goes clockwise, then the direction of moment of force is opposite to it.
7. The rule of the gimlet is very similar to the rule of a hand. Four fingers of the right hand kind of rotate the screw from r to F. The vector work will have that direction where the gimlet at such mental rotation twists.
8. Let now the point of Q be located on the same straight line which contains F force vector. Then the radius vector and a vector of force will be kollinearna. In this case their vector work degenerates in a zero vector and is represented by a point. The zero vector has no certain direction, but it is considered sonapravlenny to any other vector.