Question

A symmetric lamina of mass M consists of a square shape with a semi-circular section over each of the edges of the square, as shown. The side of the square is $2a$. The moment of inertia of the lamina about an axis through its centre of mass and perpendicular to the plane is $1.6$ $M{a}^2$. Calculate the moment of inertia of the lamina about the tangent AB in the plane of the lamina.

Answer 1

Perpendicular axis theorem $I_L+I_L+"=Io=1.6M{a}^2$.

$I_L=I_L$

$I_L=0.8M{a}^2$

Parallel axis theorem

$I_{AB}=I_L+M(a+a{)}^2$

$I_{AB}=4.8M{a}^2$