Cross Product part1

3D Model

To rotate a door you need a force. The force is composed with its two components: normal and parallel to vector r. The parallel one cannot rotate the door and can be neglected. The door is moved only by the normal component. Precisely the rotation is dependent on the so called momentum of force (M) given as the product of the length of r and the length of the normal component of F. In the model it is represented by the area of the red surface.

The door is going to rotate around the vertical dotted line. We can incorporate the direction into the concept of momentum. The momentum becomes a vector. It is directed parallely to the axis of rotation. It does not matter up or down. By convention the right hand rule and the formula:

M = r x F

are used.

M is here treated as a result of an operation on two vectors. The operation is called the cross product. Although it fulfills some rules of multiplication of numbers, it is not commutative. In the next part we will prove its distributive property.