Center of Gravity, Centroid (Composite Bodies)

Key Concept: A composite body is just a collection of attached individual bodies such

as a cylindrical bar attached to a sphere ( 3-D example) or a rectangular area of one

shape attached to a rectangular area of a different shape (2-D example).

In a Nutshell: Once again use the principle of first moments to locate the centroid of the composite body. i.e.

The moment of the sum equals the sum of the moments of individual parts.

In the case of composite bodies, use a summation approach for each individual part. The summation simply replaces the integral involved in the method of integration. i.e. for the

composite body (in this case, area, shown below)

( Σ m_i ) x_cg = Σ m_i x_cgi or (m₁ + m₂) x_cg = m₁ x_cg1 + m₂ x_cg2

( Σ m_i ) y_cg = Σ m_i y_cgi or (m₁ + m₂) y_cg = m₁ y_cg1 + m₂ y_cg2

Here m₁ is the mass of part 1, m₂ is the mass of part 2, x_cg is the x-coordinate of

the centroid for the composite, y_cg is the y-coordinate of the centroid for the composite,

x_cg1 is the x-coordinate of the centroid for part 1, x_cg2 is the x-coordinate of the centroid

for part 2, y_cg1 is the y-coordinate of the centroid for part 1,and y_cg2 is the y-coordinate

of the centroid for part 2

Also note: If the composite body involves a “void” such as a hole in the composite, then

the void has a negative contribution in the calculation.

Click here for examples.

Return to Notes on Statics

Copyright © 2019 Richard C. Coddington
All rights reserved.