Four thin rods of length L and mass m are connected as shown to form a square. A

Question

Four thin rods of length L and mass m are connected as shown to form a square. A pivot point is located in the upper corner, and the entire structure oscillates back and forth about the pivot point. Each rod is of uniform density and has a moment of inertia of 1/12mL^2, when the rod is rotated about its center of mass on an axis perpendicular to the plane of the paper. A. Calculate the moment of inertia of the structure at the pivot point. B. Find the period of the structure when it undergoes simple harmonic motion with a small angular displacement.

Explanation / Answer

I = I1 + I2 + I3 + I4
I1 = 1/3 Ml^2
I2 = 1/3 Ml^2
I3 = 1/3 Ml^2 + 5/2Ml^2
I3= 1/3 Ml^2 + 5/2 Ml^2

I = 19/3 Ml^2

T = 2[I / mg L]

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