Angles of rotation

Studies have been made on the rate of growth of oxide films on different crystal faces of a metal using ellipsometric methods. The rate was indeed different for (100), (101), (110), and (311) faces of copper [162] moreover, the film on a (311) surface was anisotropic in that its apparent thickness varied with the angle of rotation about the film normal. 

The formalism that we have set up to describe chain flexibility readily lends itself to the problem of hindered rotation. Figure 1.8a shows a sawhorse representation of an ethane molecule in which the angle of rotation around the bond is designated by electron repulsion between the atoms bonded to... 

Because of the variation in potential energy with the angle of rotation, not all locations on the rim of the cones in Fig. 1.7b are equally favored. The probability of a particular angular position depends on the potential energy at that location, V, and an averaging procedure which considers this angular variation must be used to modify Eq. (1.60). The result of this procedure is... 

Rotational Work. Rotational work is equal to torque (N-m) times angle of rotation (rad). Its SI unit is J. 

For a two-dimensional array of equally spaced holes the difftaction pattern is a two-dimensional array of spots. The intensity between the spots is very small. The crystal is a three-dimensional lattice of unit cells. The third dimension of the x-ray diffraction pattern is obtained by rotating the crystal about some direction different from the incident beam. For each small angle of rotation, a two-dimensional difftaction pattern is obtained. 

As with other types of rotating machinery, an axial compressor can be described by a cylindrical coordinate system. The Z axis is taken as running the length of the compressor shaft, the radius r is measured outward from the shaft, and the angle of rotation 6 is the angle turned by the blades in Figure 7-2. This coordinate system will be used throughout this discussion of axial-flow compressors. 

Since the peptide units are effectively rigid groups that are linked into a chain by covalent bonds at the Ca atoms, the only degrees of freedom they have are rotations around these bonds. Each unit can rotate around two such bonds the Ca-C and the N-Ca bonds (Figure 1.6). By convention the angle of rotation around the N-Ca bond is called phi (<[)) and the angle around the Ca-C bond from the same C atom is called psi (y). 

Figure 1.6 Diagram showing a polypeptide chain where the main-chain atoms are represented as rigid peptide units, linked through the atoms. Each unit has two degrees of freedom it can rotate around two bonds, its Ca-C bond and its N-Ca bond. The angle of rotation around the N-Ca bond is called phi (cj)) and that around the Co-C bond is called psi (xj/). The conformation of the main-chain atoms is therefore determined by the values of these two angles for each amino acid.

Note that the structures depicted in Fig. 5 are not self-similar because the angle of rotation of the faces differs for each layer. The layers should, therefore, not be called shells as they are called in the case of pure alkaline earth-metal clusters. With increasing size, the shape of the cluster will converge asymptotically to that of a perfect icosahedron. 

They are normally fitted with 10-12 blades, the blade tips inclined away from the angle of rotation. They have the advantage of being very efficient, with fan static efficiencies in excess of 80% for airfoil blades. This type of fan has a nonoverloading characteristic curve. 

Note that Tsai and Pagano s angle of rotation is oppositely defined to that in Figure 2-10, so the sine terms in Equation (2.98) are also of opposite sign. 

A final result of interest is the integral of the area under the transformed stiffness versus angle of rotation curve from <)) = 0 to <)) = 2k, that is, one complete revolution of the laminate ... 

The angle of rotation is, of course, directly proportional to the thickness of the layer of active substance through which the polarised light passes. The expression optical rotation or rotatory power is universally understood to be the observed angle of rotation produced by a column of 100 mm. of the optically active substance. If tubes of other lengths be... 

Drehungs-grad, m. degree of rotation, -kraft, /, rotatory power, -schwingtmg, /, torsional vibration, -streuung, /, rotatory dispersion, -vermogen, n, rotatory power, -winkel, m. angle of rotation. 

While the matrix R does not explicitly involve the axis of rotation along which e extends, nor the angle of rotation 6, it is known (from a theorem of Euler s) that every R is equivalent to a single rotation definable geometrically by an e and a 0. 

The determination of the angle of rotation is called polarimetry. In some cases, it can help a chemist follow a reaction. For example, if a reaction destroys the chirality of a complex, then the angle of optical rotation decreases with time as the concentration of the complex falls. 

Angle of rotation about one of the single bonds of the polymer chain (Chap. X). 

Figure 4. Potential energy curves for the Sq and S, states of BMPC as a function of the angle of rotation...

Molecules adsorbed at interfaces are in constant motion, both from the point of view of their orientation and of the dynamic exchange with the bulk solution. The distribution of orientation angle is characterized by the parameter D, see Eq. (13), or the angle of orientation Q. Complete randomness for the angle 0, the angle of rotation around the principal... 

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