## MortelBOX

### BOX Of Vectors     # Cross Products And Moments Of Force

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Cross Products and Moments of Force Ref Hibbeler 4.2-4.3 Bedford & Fowler Statics 2.6 4.3 In geometric terms the cross product of two vectors A and B produces a new vector C with a direction perpendicular to the plane formed by A and B (according to right-hand rule) and a magnitude equal to the area of the parallelogram formed using A and B as adjacent sides. And that is because torque is defined as the cross product between the radial distance from your axis of rotation and the rotational force being applied. So these are both vectors. So lets take a look at how I taught you vectors the first time and then Ill show you how thats really the same thing as what were doing here with the cross Direction of torque can be calculated by the rules of cross product. Consider the above diagram in which the angle between r vec r r and F vec F F is theta . In this case if the line of action of the force is extended and a perpendicular is dropped on it from the point of calculation of torque then this perpendicular is called

Why the moment of a force is calculated by the cross product of two vectorshow it is related And what does it means when I said that moment of a force about a point is for example 6 N.m I want simple clear explanation. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of the line of action of force from the axis of rotation. The symbol for torque is typically the lowercase Greek letter tau. When being referred to as moment of force it is commonly denoted by M. Next let us look at the application of cross product in defining a very important physical quangraphicy in mechanics called moment moment of a force. In the case of a point mgraphic m acted upon by a force F we know that the effect of F on m will be causing a translational acceleration in the direction of F governed by Newtons second law. That is

The cross product yields a vector answer which does have a direction (if youve ever used Flemings Left Hand rule to find the force acting on a current-carrying wire in a magnetic field youve found the cross product of those two vectors). The moment of a force does have a direction hence the use of the cross product. where is the position vector measured from the moment center to any point along the line of action of the force vector .The directional sense of the moment is found by first aligning the position and the force vectors tail to tail then curling the four fingers of the right hand from to with the thumb pointing in the direction of the moment vector.