Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be `(MR^(2))/(4)`. Find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

Explanation

Given `I_(x) =(MR^(2))/(4)and I_(y)=(MR^(2))/(4)`
According to perpendicular -axes theorem,
`I_(z)=I_(x)+I_(y)=2.(MR^(2))/(4)`
`=(1)/(2)MR^(2)`
According to parallel -axes theorem the moment of inertia of the disc about the axis AB, normal to the disc and passing through a point on its edge,
`I-I_(cm)+MR^(2)=I_(z)+MR^(2)=(1)/(2)MR^(2)+MR^(2)=(3)/(4)MR^(2)`