What is the moment of inertia of a square sheet of side $l$ and mass per unit area $\mu$ about an axis passing through the centre and perpendicular to its plane?

State the theorem of perpendicular axes and the theorem of parallel axes.

$A$ rigid body of mass $m$ rotates with angular velocity $\omega$ about an axis at a distance $d$ from its center of mass. The radius of gyration about an axis passing through the center of mass $G$ and parallel to the given axis is $K$. What is the rotational kinetic energy of the body?

$A$ solid cylinder has mass $M$,length $L$,and radius $R$. What is the moment of inertia of this cylinder about one of its generators?

The moment of inertia of a semicircular disc of mass $M$ and radius $R$ about the shown axis is:

Four identical uniform solid spheres,each of mass $M$ and radius $R$,are placed touching each other in a line as shown in the figure,with centers $A, B, C, D$. Let $I_A, I_B, I_C,$ and $I_D$ be the moment of inertia of the entire system of four spheres about an axis passing through the center of the respective sphere and perpendicular to the plane containing the centers. The difference $|I_A - I_B|$ is: (in $MR^2$)