Machinery's Handbook, 31st Edition
Center of Gravity
231
Area of a Parabola:
h
For the complete parabolic area, the center of gravity is on the center line or axis, and a h 5 3 = For one-half of the parabola: a h and b w 5 3 8 3 = = For the complement area ABC : . . c h and d w 03 075 = =
a
a
w
h
B
C
w
d
c
A
Cylinder:
d
T he center of gravity of a solid cylinder (or prism) with parallel end surfaces is located at the middle of the line that joins the centers of gravity of the end surfaces. The center of gravity of a cylindrical surface or shell with the base or end surface in one end is found from: a h d h 4 2 2 = + The center of gravity of a cylinder cut off by an inclined plane is located by: n tan a h h r b h r 2 8 4 2 2 2 α α = + = ta n tan a h h r b h r 2 8 4 2 2 2 α α = + = ta where α is the angle between the obliquely cut off surface and the base surface. For a solid portion of a cylinder, as shown, the center of gravity is determined by: . . a r b h 16 3 31416 32 3 31416 # # = = For the cylindrical surface only: . . a r b h 4 1 31416 8 1 31416 # # = = If the cylinder is hollow, the center of gravity of the solid shell is found by: . . a R r R r H h H h − − b 16 3 31416 32 3 31416 # # 3 3 4 4 3 3 4 4 = − − =
a
h
b
h
a
r
Portion of Cylinder:
h
r
a
b
H
r R
h
a
b
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online