Question

Three mass point m₁, m₂ and m₃ are located at the vertices of an equilateral triangle of length 'a'. What is the moment of inertia of the system about an axis along the altitude of the triangle passing through m₁?

Answer 1

Let the mass point be m₁, m₂ m₃ situated, respectively at the vertices A, B and C or the equilateral triangle ABC, each of which side is a.

Then, moment of inertia of the three-particle system about the altiude AD is,

I = m₁ x (distance of m₁ from AD) + m₂ x distance of m₂ from AD)² + m₃ x (distance of m₃ from AD)²

= m₁(0)² + m₂ (a/2)² + m₃ (a/2)² = 1/4 (m₂ + m₃)a².