Machinery's Handbook, 31st Edition
232
Center of Gravity
Center of Gravity of Two Bodies:
If the weights of the bodies are P and Q , and the distance between their centers of gravity is a , then: b P Q Qa c P Q Pa = + = + b P Q Qa c P Q Pa = + = + In a solid pyramid the center of gravity is located on the line joining the apex with the center of gravity of the base surface, at a distance from the base equal to one-quarter of the height; or a = 1 ∕ 4 h . The center of gravity of the triangular surfaces forming the pyramid is located on the line joining the apex with the center of gravity of the base surface at a distance from the base equal to one-third the height: a = 1 ∕ 3 h . The center of gravity is located on the line that joins the centers of gravity of the end surfaces. If A 1 = area of base surface, and A 2 area of top surface, a A A A A h A A A A 4 2 3 1 1 2 2 1 1 2 2 # # = + + + + _ _ i i The same rules apply as for the pyramid. For the solid cone: a h 4 1 = For the conical surface: a h 3 1 = The same rules apply as for the frustum of a pyramid. For a solid frustum of a circular cone the formula below is also used: a R Rr r h R Rr r 4 2 3 2 2 2 2 = + + + + ^ ^ h h The location of the center of gravity of the conical surface of a frustum of a cone is determined by: a R r h R r 3 2 = + + ^ ^ h h
a
P
Q
b
c
Pyramid:
h
h
Frustum of Pyramid:
A 2 = Area of Top
h
a
A 1 = Area of Base
Cone:
h
a
Frustum of Cone:
r R
r
h
a
R
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online