Four identical rods, each of mass `m` and length `l`, make a square frame in the `xy` plane as shown in Fig.
a. Calculate its moment of inertia about the `x`-and y-axes.
b. Also, calculate its moment of inertia about the `z`-axis.

Explanation

a. Due to symmetry the moment of inertia of the square frame about the `x`- and `y`-axes are equal i.e., `I_(x)=I_(y)`
Now `I_(x)=0+2[(ml^(2))/3]+ml^(2)=ml^(2)`
`I_(y)=I_(x)=5/3ml^(2)`
b. Due to perpendicular axis theorem
`I_(z)=I_(x)+I_(y)=5/3ml^(2)+5/3ml^(2)=10/3ml^(2)`
Note that the `z`-axis does not pass through its centre of mass.