Question

In the diagram shown here, all three rods are of equal length L and equal mass M. the system is
rotted such that rod B is the axis of rotation. What is the momentum of inertia of the system?​

Answer 1

The momentum of inertia of the system is I =  1 /2 M L ^2  

Explanation:

• The moment of inertia of a single rod about an axis passing through its center and perpendicular to it is  = 1/2 M L ^2
• Each side of the equilateral triangle about an axis passing through the triangle's center and perpendicular to its plane is
• 1 /12 M L ^2 +  M ( L /2 √ 3 )^ 2 =  1 /6 M L^ 2
• The moment of inertia is then
• 3 x 1/2 ML^2  =  1 /2 M L ^2

Thus the momentum of inertia of the system is I =  1 /2 M L ^2  

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