Centres of gravity

One of the most important fiinctions in the application of light scattering is the ability to estimate the object dimensions. As we have discussed earlier for dilute solutions containing large molecules, equation (B 1.9.38) can be used to calculate tire radius of gyration , R, which is defined as the mean square distance from the centre of gravity [12]. The combined use of equation (B 1.9.3 8) equation (B 1.9.39) and equation (B 1.9.40) (tlie Zimm plot) will yield infonnation on R, A2 and molecular weight. 

The moment of inertia / of any molecule about any axis through the centre of gravity is given by... 

From an FMEA of the system design, a Severity Rating S) = 1 was allocated, relating to a safety critical failure in service. It is required to find the optimum unequal angle section size from the standard sizes available. It is assumed that the load is carried at the section s centre of gravity, G, and only stresses due to bending of the section are considered, that is, the torsional effects are minimal. The combined weight of the beam and tie rod are not to be taken into account. 

In terms of the dimensions, a, b and t for the section, several area properties can be found about the x-x and y-y axes, such as the second moment of area, 4, and the product moment of area, 4y. However, because the section has no axes of symmetry, unsymmetrical bending theory must be applied and it is required to find the principal axes, u-u and v-v, about which the second moments of area are a maximum and minimum respectively (Urry and Turner, 1986). The principal axes are again perpendicular and pass through the centre of gravity, but are a displaced angle, a, from x-x as shown in Figure 4.63. The objective is to find the plane in which the principal axes lie and calculate the second moments of area about these axes. The following formulae will be used in the development of the problem. 

We may also speak of the pressure at a point in the interior of a mass of liquid or gas, because if a very small plane area removed from the immediate vicinity of one side, a definite force P must be applied to keep the area in position. From the principle of reaction we see that each of the two portions of fluid divided by an im a(f in ary plane opposite forces is called a stress. 

Corollary.—The point M is the centre of gravity of weights 1 — m and m placed at the liquid and vapour ends of the line of heterogeneous states. 

Fig. 3.12. The room temperature CARS spectra of CH4 obtained in [162] at the following densities (1) 0.1 amagat of pure CH4 (2) 5 amagat CH4 (3) 5 amagat CH4 + 35 amagat Ar (4) 5 amagat CH4 + 85 amagat Ar. The position of the vibration frequency wv is indicated as well as the centre of gravity of the Q0i branch rotational structure wv + coq.

Without any restrictions we may shift the origin of the frequency scale to the centre of gravity of the spectrum ... 

Ancillary equipment attached to a tall vessel will subject the vessel to a bending moment if the centre of gravity of the equipment does not coincide with the centre line of the vessel (Figure 13.21). The moment produced by small fittings, such as ladders, pipes and manways, will be small and can be neglected. That produced by heavy equipment, such as reflux condensers and side platforms, can be significant and should be considered. The moment is given by ... 

Figure 13.49. Displacement of centre of gravity of a centrifuge bowl...

At high speeds deflection decreases till centre of gravity comes into vertical axis... 

Figure 13.50. Diagram of action of self-balancing centrifuge, showing motion of centre of gravity and...

An inflatable bellows used in a pneumatic suspension system for motor transport irrespective of load the centre of gravity of the vehicle can be maintained at a constant height above ground level with appropriate control systems. 

Fig. 2.21 Compartmental burden [t] (left panel), solid lines model experiment with aggregation of marine snow (AGG), dashed lines experiment with satellite assimilation (SAT). Migration of the centre of gravity of the total environmental burden (right panel). Dashed lines show the location of the COG at the end of the simulation. The COG of the SAT experiment is shown in blue, the COG of the AGG experiment in red. Circles represent monthly mean COGs.

What is the distribution function for the velocity of the centre of gravity ... 

Rotational degrees of freedom result from the rotation of a molecule about an axis through the centre of gravity. 

Stable, metastable and unstable states a simple analogy. A simple mechanical model is shown in Fig. 2.37 a block on a stand may be in different equilibrium states. In A and C the centre of gravity (G) of the block is lower than... 

Figure 2.37. A simple mechanical system and its equilibrium states. Different positions of a block on a stand and the corresponding values of the gravitation potential energy are shown. Point G is the centre of gravity of the block. In A there is stable equilibrium, in C metastable, in B unstable.

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