A rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 4.0 s. Assume R = 0.90 m and m = 3.0 kg, calculate the structure's rotational inertia about the axis of rotation.
I_rods = (1/12)ML^2
I_hoop = (1/2)MR^2
I = I_rods + I_hoop
The Attempt at a Solution
The third equation is constructed by noticing that the problem states that the structure consists of both the square made of thin rods and the hoop. The square only has two rods that have moments of inertia because two are perpendicular to the axis and the other two are parallel, which have a moment of inertia of 0 (at least that is what I have been told). So...
I = 2[I_rods] + I_hoop
I = 2[(1/12)(3 kg)(0.90 m)^2] + (1/2)(3 kg)(0.90 m)^2
I = 2.835 kg*m^2
I know this is wrong and it has to do with my equations. Please help. Thanks for your time.