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.

Given the moment of inertia of a disc of mass M and radius R about any

1.	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.
Answer» Solution :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 THEMOMENT 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)`