Video: Identifying the Position of the Center of Mass of a Uniform Triangular Lamina

Where does the center of gravity of a uniform triangular lamina lie?

01:09

Video Transcript

Where does the center of gravity of a uniform triangular lamina lie?

Let’s firstly consider the scaling triangle 𝐴𝐡𝐢 as shown. If 𝐴 has coordinates π‘₯ one, 𝑦 one; 𝐡 has coordinates π‘₯ two, 𝑦 two; and 𝐢 has coordinates π‘₯ three, 𝑦 three. We know that the center of gravity lies at the point π‘₯ one plus π‘₯ two plus π‘₯ three divided by three, 𝑦 one plus 𝑦 two plus 𝑦 three divided by three. This point occurs at the intersection of the medians.

The median from vertex 𝐴 bisects the line 𝐡𝐢. Likewise, the median from 𝐡 bisects the line 𝐴𝐢. Finally, the median from 𝐢 bisects the line 𝐴𝐡. The intersection of these three lines is the center of gravity of a uniform triangular lamina.

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