Machinery's Handbook, 31st Edition
230
Center of Gravity
Circle Sector:
Distance b from center of gravity to center of circle is: . sin b l rc A r c r 3 2 3 38197 2 α α = = = in which A = area of sector, and α is expressed in degrees. For the area of a half-circle: . b r r 4 3 04244 ' π = = For the area of a quarter-circle: . b r r 4 2 3 06002 # ' π = = For the area of a sixth of a circle: . b r r 2 06366 ' = π = Distance b from center of gravity to center of circle is: . sin b R r R r 38197 2 2 3 3 α α = − − ^ ^ h h Angle α is expressed in degrees.
c
r
l
b
Part of Circle Ring:
R
r
b
Spandrel or Fillet:
R
. . 02234 02234
x y
R R
= =
2
Area
. 02146
R
=
y
x
Segment of an Ellipse: B
The center of gravity of an elliptic segment ABC , symmetrical about one of the axes, coincides with the center of gravity of the segment DBF of a circle, the diameter of which is equal to that axis of the ellipse about which the elliptic segment is symmetrical.
A
C
D
F
Spherical Surface of Segments and Zones of Spheres:
h H
Distances a and b which determine the center of gravity are: a h b H 2 2 = = a h b H 2 2 = =
a
b
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