## Gyration Sentence Examples

- Since I~=Ii., I~=o, we deduce 100=3/4Ma2, ~ =4MaZ; hence the value of the squared radius of
**gyration**isfora diameter 3/4ai, and for the axis of symmetry 3/4af. - Which we shall meet with presently as the ellipsoid of
**gyration**at G. - In the case of an axial moment, the square root of the resulting mean square is called the radius of
**gyration**of the system about the axis in question. - From its axis (0), if the radius of
**gyration**about a longitudinal axis through G, aiid 0 the inclin - ation of OG to the vertical, FIG. - The radius of
**gyration**of the section is 2a 2. - This is called the ellipsoid of
**gyration**at 0; it was introduced into the theory by J. - If M be the total mass, k the radius of
**gyration**(~ ii) about the axis, we have sin 0, (3) - R is called the radius of
**gyration**of the body with regard to an axi: - After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of
**gyration**k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %. - The square of the radius of
**gyration**with respect to a diameter is ia2. - The formula (16) expresses that the squared radius of
**gyration**about any axis (Ox) exceeds the squared radius of**gyration**about a parallel axis through G by the square of the distance between the two axes. - The squares of the radii of
**gyration**about the principal axes at P may be denoted by k,i+k32, k,f + ki2, k12 + k,2 hence by (32) and (35), they are rfOi, r2Oi, r20s, respectively. - It possesses thi property that the radius of
**gyration**about any diameter is half thi distance between the two tangents which are parallel to that diameter, In the case of a uniform triangular plate it may be shown that thi momental ellipse at G is concentric, similar and similarly situatec to the ellipse which touches the sides of the triangle at their middle points. - If k be the radius of
**gyration**about p we find k2 =2Xarea AHEDCBAXONap, where a$ is the line in the force-diagram which represents the sum of the masses, and ON is the distance of the pole 0 from this line. - If K be the radius of
**gyration**about a parallel axis through G, we have kf=K2+h2 by If (16), and therefore i=h+K1/h, whence GO.GP=K2.