Question

Moment of inertia of three uniform rods of mass M and length l joined to form an equilateral triangle, about an axis passing through one of its sides.

Answer 1

Moment of Inertia of a single rod = 1/12 *M*L²

According to parallel axes theorem, each side of the equilateral triangle about an axis passing through the triangle's center and perpendicular to its plane is;

⇒ 1/12*M*L²+M*(L²√3)²=1/6*M*L²

Moment of inertia of the triangle about the axis of three sided equilateral triangle is;

⇒ 3*1/6*M*L²

I = 1/2*M*L²