The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis touching the disc at its diameter and normal to the disc is

The moment of inertia of a uniform cylinder of length $l$ and radius $R$ about its perpendicular bisector is $I$. What is the ratio $l/R$ such that the moment of inertia is minimum?

The moment of inertia of a solid cylinder about its own axis is the same as its moment of inertia about an axis passing through its centre of gravity and perpendicular to its length. The relation between its length $L$ and radius $R$ is

Seven identical coins are rigidly arranged on a flat table in the pattern shown below,so that each coin touches its neighbours. Each coin is a thin disc of mass $m$ and radius $r$. Note that the moment of inertia of an individual coin about an axis passing through its centre and perpendicular to the plane of the coin is $\frac{m r^2}{2}$. The moment of inertia of the system of seven coins about an axis that passes through the point $P$ (the centre of the coin positioned directly to the right of the central coin) and perpendicular to the plane of the coins is ..........$m r^2$.

The moment of inertia of a uniform semicircular wire of mass $m$ and radius $r$,about an axis passing through its centre of mass and perpendicular to its plane is ..........

Calculate the moment of inertia of an annular disc about an axis tangent to the outer circle and lying in the plane of the disc. The mass of the disc is $M$,the inner radius is $R_1$,and the outer radius is $R_2$.