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Question

Three identical uniform rods each of length 1 m and 2 kg are arranged to from an equilateral triangle. What is the moment of inertia of the system about an axis passing through one corner and perpendicular to the plane of the triangle?

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Solution

Mol of rod passing through the center = 112ML2

mol of rod passing through one side = 13ML2

AP = 32 L

MoI of BC through the perpendicular A

= 112ML2+M(32L)2

= 112ML2+34ML2

= 56ML2

By the principal of superposition

= 13ML2+13ML2+56ML2

= 96ML2

= 32ML2

radius of gyration

K = 32ML23M

= L2

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