Proper rotation

If we represent the motion in the pg-plane, this integral is to be taken over the straight line p = const., not over a closed curve. But we must observe that in this plane points with the same p, whose g-co-ordinates differ by 27t, represent the same state of the rotator. Properly speaking, therefore, we should consider, not a y>g -plane but a g-cylinder (fig. 5) of circumference 27t, so that the integral has now to be taken over the circumference of the cylinder, and has the... 

Rotor may not rotate properly if fluid viscosity is high or flow is laminar ... 

By bubbles in fluid rotor may not rotate properly). Hence the temperature of liquid should be much lower than boiling point during flow measurement. 

In terms of these operators, the translations can be described as BIR (where E is the identity, or unit element), while the pure rotations (proper or improper) are... 

The scan area" field which is white at the start of scanning is painted black during the test so that the inspector will immediately see which areas still remain to be tested. The zone has not been 100% scanned until the entire field is black. If the probe movement is too fast, or if there is no coupling, or if the probe is rotated at too large an angle, there is no change in the color this means that the corresponding zone has not been properly scanned. 

However, the Yj m are not the eorresponding eigenfunetions beeause the operator P now eontains eontributions from rotations about three (no longer two) axes (i.e., the three prineipal axes). The proper rotational eigenfunetions are the DJm,k funetions... 

To verify that the Fischer jjrojection has the R configuration at its chirality center rotate the three dimensional representation so that the lowest ranked atom (H) points away from you Be careful to maintain the proper stereochemical relationships during the operation... 

FIGURE 7 9 Repre sentations of (2/ 3R) dihy droxybutanoic acid (a) The staggered conformation is the most stable but is not properly arranged to show stereochemistry as a Fischer projection (b) Rotation about the C 2-C 3 bond gives the eclipsed conforma tion and projection of the eclipsed conformation onto the page gives (c) a correct Fischer projection... 

Notice that the eclipsed conformation of d ribose derived directly from the Fischer pro jection does not have its C 4 hydroxyl group properly oriented for furanose ring forma tion We must redraw it m a conformation that permits the five membered cyclic hemi acetal to form This is accomplished by rotation about the C(3)—C(4) bond taking care that the configuration at C 4 is not changed... 

As viewed m the drawing a 120° counterclockwise rotation of C 4 places its hydroxyl group m the proper position At the same time this rotation moves the CH2OH group to a position such that it will become a substituent that is up on the five membered ring The hydrogen at C 4 then will be down m the furanose form... 

---