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Wize University Statics Textbook (Master) > Center of Gravity and Centriod

Optional: Centroids vs. Center of Mass

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The concept of a centroid and the concept of a centre of mass/gravity/weight are often confused together. Though the concepts are similar, they're not identical. Let's begin by defining the difference:

  • The centroid is the geometric centre of a given shape/object - it will depend on the geometry
  • The center of mass is where weight acts on a body - it will depend on both the geometry as well as the material used in a given body
For cases where the density of objects is uniform, the centroid and the centre of mass will coincide. We've covered such cases in another section. In this section, we will focus on how we can determine the centre of mass of a body of multiple materials (varying density). The setup and the process is really similar to solving compound geometric centroid questions, with a slight adjustment - instead of using an area weighted average, we use a weight weighted average. This can be best shown in an example.

Note: we will only consider centre of mass problems for compounded geometric shapes (no integration).
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A 30 mm x 25 mm block of wood (density = 850 kg/m3) is attached to a 30 mm x 5 mm steel plate (density = 6000 kg/m3). Determine the centre of mass of the compounded beam:


Pwood = 850 kg/m3

μsteel =6000 \mu_{steel}\ =6000\ kg/m3

Pplusher = 950 kg/m3



Ai Pi μi‾\underline{\mu_i} y‾‾\overline{\underline{y}} μi y‾‾\underline{\mu_{i\ \overline{y}}}
(1) (15)(25) (6000) 2250 7.5 16
(2) -(15)(10) (6000) -900 5 875
(3) (15)(10) (850) 127.5 5 637.5
375 1477.5 13012.5
y‾=8.81 cm\overline{y}=8.81\ cm


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A wooden block measuring 15 cm x 10 cm in cross section is placed inside a steel channel as shown below. The compounded beam has external dimensions of 25 cm x 15 cm. The density of wood is 850 kg/m3 and the density of steel is 6000 kg/m3. Find the centre of mass of the cross section.


Quiz: Center of Mass Practice Question
A dual glass pane includes two layers of glass with a plastic layer in between. The two glass panes have a thickness of 3 mm and 6 mm respectively, and the plastic layer is 2 mm thick in between. the density of glass and plastic is 2700 and 800 kg/m3 respectively. What is the distance between the centroid and the centre of mass for a uniform cross section of this material?

Enter your answer in mm.