ROTATION
, Rolling, in Mechanics. See ROLLING.
Rotation, in Geometry, the circumvolution of a surface round an immoveable line, called the axis of Rotation. By such Rotation of planes, the figures of certain regular solids are formed or generated. Such as, a cylinder by the Rotation of a rectangle, a cone by the Rotation of a triangle, a sphere or globe by the Rotation of a semicircle, &c.
The method of cubing solids that are generated by such Rotation, is laid down by Mr. Demoivre, in his specimen of the use of the doctrine of fluxions, Philos. Trans. numb. 216; and indeed by most of the writers on Fluxions. In every such solid, all the sections perpendicular to the axis are circles, and therefore the fluxion of the solid, at any section, is equal to that circle multiplied by the fluxion of the axis. So that, if x denote an absciss of that axis, and y an ordinate to it in the revolving plane, which will also be the radius of that circle; then, n being put for 3.1416, the area of the circle is ny2, and consequently the fluxion of the solid is ny2x.; the fluent of which will be the content of the solid.
Such solid may also be expressed in terms of the generating plane and its centre of gravity; for the solid is always equal to the product arising from the generating plane multiplied by the path of its centre of gravity, or by the line described by that centre in the Rotation of the plane. And this theorem is general, by whatever kind of motion the plane is moved, in describing a solid.
Rotation, Revolution, in Astronomy. See REVOLUTION.
Diurnal Rotation. See Diurnal, and Earth.
