# Rotating sheet

**Classical Mechanics**Level 3

Consider a rectangular sheet of metal with width \(W=2~\mbox{m}\) and length \(L=5~\mbox{m}\). The sheet is in the x-y plane, with the origin right in the geometric middle of the sheet. The x-axis is parallel to the short edge, while the y-axis is parallel to the long edge. The moment of inertia about the z-axis is \(I_z=10~\mbox{kg}\cdot\mbox{m}^2\) and the moment of inertia about an axis that passes diagonally through the sheet (i.e. corner to corner) in the xy plane is \(I=5~\mbox{kg}\cdot\mbox{m}^2\). What is the moment of inertia about the y-axis in \(\mbox{kg}\cdot\mbox{m}^2\)?