Solid of revolution

These theorems are useful for determining volumes V and surface areas S of solids of revolution if the centers of gravity are known. If S and V are known, the centers of gravity may be determined. 

A shell of revolution is the form swept out by a line or curve rotated about an axis. (A solid of revolution is formed by rotating an area about an axis.) Most process vessels are made up from shells of revolution cylindrical and conical sections and hemispherical, ellipsoidal and torispherical heads Figure 13.3. 

The lens consists of two parts, each of which is generated as a solid of revolution by rotating the semi-circle x2 + y2 = r2 about Ox. The resulting solid body has the volume... 

If the particle is a solid of revolution its center of reaction lies along the axis (say the Rxy axis). At this point the coupling dyadic vanishes, while both the translation and rotation dyadics at any point along the axis each adopt the general form... 

The correct treatment of rotations is somewhat difficult and gives rise to series which have no simply expressible sum. For a rigid rotator which is a solid of revolution of moment of inertia / and which, for reasons which will emerge later, must not consist of two identical atoms, the following simple treatment is possible. 

The volume T of a solid of revolution generated by rotating a plane figure F about an external axis is equal to the product of the area A of f and the distance d traveled by its geometric centroid. 

Fig. 6.6 (a) Plotting the matter capacity B as a function of chemical potential /t, (b) Exchanging axes, (c) Solid of revolution having the same content. 

Such bodies are also called solids of revolution. 

To demonstrate solids of revolution, a group of students were assigned to prepare a working model in which the plane surfaces when rotated about an axis, which appears as solid. 

Figures 3.8 and 3.9 present a system to identify the shape classification used, in order to determine Cc- The first step is to read the supporting notes and complexity definitions provided in Figure 3.8. There are three basic shape categories solid of revolution, prismatic solid and flat or thin wall section components. These three fundamental shape categories can be sub-divided into five bands of complexity as shown pictorially in Figure 3.9. The classifica-...

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