Right-hand screw rule

We saw in Section 1.3.2 and in Figure 1.5 how the orbital angular momentum of an electron can be represented by a vector, the direction of which is determined by the right-hand screw rule. 

Angular momenta transform like vectors, the directions of the vectors being the directions of the axes about which the angular momenta are determined. It is customary to take the sense of the vectors such as to correspond to the right-hand screw rule. 

Rgure 5.2 The right-hand screw rule for determining the direction of the angular velocity or angular momentum vector... 

Remember that the angular momentum L of an MP (an electron, in our case) relative to an origin (nucleus) is defined as a vector product L = [r p], where r is the electron radius vector relative to the nucleus, and p the linear electron momentum (p = tm). On traveling along a circular orbit the linear velocity is perpendicular to r (w T r), then L, = IL,I = mor. The direction of the vector L, is defined by the rule of vector product (the right-hand screw rule). 

The enantiomers shown are related as a right-hand and left-hand screw, respectively. Chiral allenes are examples of a small group of molecules that are chiral, but don t have a chirality center. What they do have is a chirality axis, which in the case of 2,3-pentadiene is a line passing through the three carbons of the allene unit (carbons 2, 3, and 4). The Cahn-Ingold-Prelog R-S notation has been extended to chiral allenes and other molecules that have a chirality axis. Such compounds are so infrequently encountered, however, we will not cover the rules for specifying their stereochemistry in this text. 

If we go back to the Eq. (325) defining the viscosity, both the torque and the angular velocity are represented by axial vectors or pseudovectors. This is because they actually have no directional property at all (as polar vectors have), but are instead connected to a surface in space within which a rotation can only be related to a (perpendicular) direction by a mere convention like the direction for the advance of a screw, right-hand rule , etc. In fact they are tensors of second rank which are antisymmetric, which means that... 

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