Let Q - the point about which the torque is considered.This point is called a pole.Spend the radius vector r from this point to the point of application of force F .Then torque M is defined as the cross product r on F : M = [rF] .
The result is a vector cross product.The length of the module is expressed by: | M | = | r | · | F | · sinφ, where φ - the angle between the vectors r and F .Vector M both orthogonal vector r , and vector F : M ⊥ r , M ⊥ F .
Directed vector M so that the triple vector r , F , M is right.How to determine that the triple vector is right?Imagine, if you (your eye) are at the end of the third vector and look at the two other vectors.If the shortest possible transition from the first to the seco
nd vector appears to be originating counterclockwise, then it is a right-handed vectors.Otherwise, you're dealing with the left three.
So align the start vectors r and F .This can be done by parallel translation vector F at Q. Now, through this same point swipe axis perpendicular to the plane of the vectors r and F .This axis is perpendicular to both vectors at once.Here are possible in principle only two options direct torque: up or down.
Try to direct the time of the force F up, draw the arrow on the axis vector.Out of this would look like arrows on vector r and F (can draw a symbolic eye).The shortest transition from r to F can designate a rounded arrow.Is the triple of vectors r , F , M right?The arrow indicates the direction of counterclockwise?If yes, then you have chosen the right direction for the moment force F. If not, then we need to change in the opposite direction.
determine the direction of the moment of force can also right-hand rule.Align the index finger with the radius vector.Middle finger to align the force vector.Since the end of the thumb raised up look at the two vectors.If the transition from the middle finger to the forefinger is performed counterclockwise, the direction of the moment of force coincides with the direction which indicates the thumb.If the transition goes clockwise, the direction of the moment of force opposite to it.
right-hand rule is very similar to the right hand.The four fingers of his right hand as though turn the screw on r to F .The vector product will be the direction in which the gimlet is twisted in such a mental rotation.
Suppose now that the point Q is located on the same line that contains the force vector F .Then the radius vector and the force vector will be collinear.In this case, their cross product degenerates into zero vector and represented by a point.The zero vector has no specific direction, but it is codirectional any other vector.
- «Mechanics", DVSivukhin, 2006.
- «Elements of linear algebra and analytic geometry," RFApatenok, 1986.
- «The course of analytical geometry and linear algebra", DVBeklemishev, 2001.
- how to calculate the torque