Machinery's Handbook, 31st Edition
Center of Gravity
233
Wedge:
c
The center of gravity is on the line joining the center of gravity of the base with the middle point of the edge, and is located at: a b c h b c 2 2 = + + ^ ^ h h
h
a
b
Paraboloid:
The center of gravity of a solid paraboloid of rotation is at: a h 3 1 =
a
h
Half of a Hollow Sphere:
The center of gravity is located at: a R r R r 3 3 4 4 =
8 3
h h
− − ^ ^
a r R
Spherical Segment:
The center of gravity of a solid segment is determined by: a 2 = − ^ h
h
r h h r h 4 3 3 2 4 3 4 − − ^ ^ ^
r h r h −
b
h
a
h h
r
b
=
For a half-sphere, a = b = 3 ∕ 8 r
Spherical Sector:
r
The center of gravity of a solid sector is at: cos a r r h 8 3 1 8 3 2 α = + = − ^ ^ h h
a
h
Segment of Ellipsoid or Spheroid: B
The center of gravity of a solid segment ABC , symmetrical about the axis of rotation, coincides with the center of gravity of the segment DBF of a sphere, the diameter of which is equal to the axis of rotation of the spheroid.
A
C
D
F
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