A rod of length 4L consists of steel rod of mass 4M, bent Into the shape of an s

Question

A rod of length 4L consists of steel rod of mass 4M, bent Into the shape of an square of length L on each side (so each side has a mass of M). This square is suspended from one its corners. Make a detailed analysis of the problem What is the moment of inertia of the square about an axis through this corner and perpendicular to its plane? You can use the moment of inertia formula (or a rod. (Use problem solving techniques) A small disturbance is applied to the square, and it starts an oscillatory motion about the same axis under gravitation. Determine the natural frequency of this oscillation for small amplitude oscillations. Make the checks of your results.

Explanation / Answer

MOI of square abt COM = (2ma^2)/12 = ma^2/6 .. If u consider the two diagonals as x and y axes then the axis abt which MOI has been found becomes z-axis.. Now Ix = Iy because both the diagonals(MOI abt both) are same by symmetry Hence 2Ix = ma^2/6 Hence I = ma^2/12

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